Speaking at a news conference while on an official visit to Finland, Mr. Putin offered no new information on where Mr. Snowden might be headed from the transit area of Sheremetyevo Airport in Moscow. But he said Mr. Snowden had broken no Russian laws. 

“Mr. Snowden is a free man,” Mr. Putin said, according to Russian news services traveling with him. “The faster he chooses his ultimate destination, the better for us and for him.” 

He also said that Russia’s special security services “are not engaged with him and will not be engaged,” despite Mr. Snowden’s trove of American intelligence documents. 

“On the territory of the Russian Federation, Mr. Snowden, thank God, did not commit any crime,” Mr. Putin said. “As for the issue of the possibility of extradition,” Mr. Putin said, “we can only send back some foreign nationals to the countries with which we have the relevant international agreements on extradition. With the United States we have no such agreement.” 

Mr. Putin spoke hours after the Russian foreign minister, Sergey V. Lavrov, chastised the United States for its demands regarding Mr. Snowden, whose successful effort, so far, to elude his American pursuers has captivated global attention, showed the limits of American power and strained American relations with Russia and China. Mr. Snowden flew to Moscow on Sunday from Hong Kong despite an American request that the authorities there arrest him. 

Mr. Snowden has been charged with violating American espionage laws by revealing secret information on intelligence-gathering. He and his allies describe him as a whistle-blower whose revelations have exposed what they called the United States government’s invasion of privacy around the world. 

Mr. Lavrov said Mr. Snowden had not crossed the Russian border, which appeared at first to be a denial that he was in Russia. But it also was a technical way of saying Mr. Snowden was in the international passenger transit area, a restricted zone where foreign travelers do not get their passports stamped and do not pass through immigration checkpoints as they await flight connections to other countries. Mr. Putin’s remarks were far more direct. 

American officials, including Secretary of State John Kerry, lashed out with unusual force on Monday against China for allowing Mr. Snowden to leave Hong Kong, against Russia for reportedly permitting him safe transit and against Ecuador for declaring that it is actively considering Mr. Snowden’s request for political asylum. The Americans have demanded that he be seized and repatriated. 

“He didn’t cross the Russian border, and we consider the attempts we are seeing to accuse the Russian side of violating United States law as completely ungrounded and unacceptable, or nearly a conspiracy accompanied by threats against us,” Mr. Lavrov said, speaking to reporters here after a meeting with the Algerian foreign minister. He added, “There are no legal grounds for this kind of behavior from American officials toward us.” 

Later in the day Mr. Kerry, speaking to reporters while visiting Saudi Arabia, sought to tone down the angry exchange of words with his Russian counterpart, with whom he has sought to cultivate a good relationship. “We are not looking for a confrontation,” Mr. Kerry said. 

The comments by Mr. Putin and Mr. Lavrov were the first by top Russian officials about Mr. Snowden since Mr. Snowden’s reported arrival at Sheremetyevo Airport in Moscow on Sunday. Employees of Aeroflot, the Russian airline, said Mr. Snowden had been booked on an afternoon flight Monday to Havana, but he did not board and the aircraft left without him. 

Ecuador confirmed that it had received an asylum request and had provided documents allowing Mr. Snowden to travel there. Mr. Snowden’s American passport has been revoked. 

Russian officials on Monday said that they had no information about Mr. Snowden, which seemed unlikely at the time given that the Russian police took the unusual step of standing on the tarmac surrounding the plane that reportedly was supposed to take him to Cuba. Russian authorities also cordoned off the gate and had threatened to take telephones from journalists preparing to board the flight.

The sharp tone of comments by Mr. Kerry and other American officials was surprising, in part because there was no reason to believe that they could force Russia to cooperate and because it is highly unlikely that, if the roles were reversed, the United States would readily repatriate a Russian fugitive security official reportedly carrying computers filled with government secrets. 

The United States and Russia, fierce rivals on intelligence matters dating to the cold war, have long shown an ability to maintain their broader bilateral relationship in the face of occasional disputes over espionage incidents, including the arrest last month in Moscow of an American Embassy employee accused of working as an operative for the Central Intelligence Agency. But Mr. Lavrov’s pointed remarks indicated that the diplomatic contretemps was taking a nasty turn. 

On Monday, the United States accused Russia of ignoring the law in allowing Mr. Snowden to travel through the Moscow airport and sharply criticized Russia, China and Ecuador over their records on Internet freedom. 

Mr. Lavrov said on Tuesday, “We have no connection with Mr. Snowden, nor with his relation toward the American justice system, nor with his movement around the world. He chose his own route and we, like most of those here, found out about this from the press.” 

The anti-secrecy organization, WikiLeaks, which says it has helped Mr. Snowden evade the American authorities, has said that he is safe and healthy but has declined to pinpoint his whereabouts. The White House has said it believes that Mr. Snowden is still in Moscow. 

American officials also openly mocked China and Russia on Monday as states that repress free speech and transparency and therefore are hardly apt refuges for someone fighting government secrecy in the United States. 

“I wonder if Mr. Snowden chose China and Russia as assistants in his flight from justice because they’re such powerful bastions of Internet freedom,” Mr. Kerry said sarcastically during a stop in New Delhi. 

President Obama’s press secretary, Jay Carney, said Mr. Snowden’s chosen destinations indicated “his true motive throughout has been to injure the national security of the United States.” 

The strong words went beyond typical diplomatic language and underscored the growing ramifications of the case for the United States. The Obama administration’s inability, at least for now, to influence China, Russia and countries in Latin America that may accept Mr. Snowden for asylum, like Ecuador, brought home the limits of American power around the world. 

Ecuador’s foreign minister, Ricardo Patiño, criticized the United States on Monday for its pursuit of Mr. Snowden. “The one who is denounced pursues the denouncer,” Mr. Patiño said at a news conference in Hanoi, Vietnam, a stop on a previously scheduled diplomatic visit to Asia. “The man who tries to provide light and transparency to issues that affect everyone is pursued by those who should be giving explanations about the denunciations that have been presented.” 

Ecuador’s president, Rafael Correa, wrote on his Twitter account, “We will analyze very responsibly the Snowden case and with absolute sovereignty will make the decision we consider the most appropriate.” The United States remains Ecuador’s leading trading partner, but Washington’s influence in Quito has been slight since Mr. Correa became president in 2007. He has repeatedly flouted and tweaked the United States, by, for example, stopping American antidrug flights out of a military base in Manta, and expelling the American ambassador in 2011 after WikiLeaks cables suggested she felt Mr. Correa had tolerated police corruption. 

A range of American officials, including the deputy secretary of state and the F.B.I. director, spent Monday reaching out to their Russian counterparts seeking cooperation, without any apparent result. Mr. Snowden, who spent Sunday night in the transit zone of Sheremetyevo Airport, did not board the flight for Havana and he made no public appearance or statement. 

American intelligence officials remained deeply concerned that Mr. Snowden could make public more documents disclosing details of the National Security Agency’s collection system or that his documents could be obtained by foreign intelligence services, with or without his cooperation.

Technical experts have been carrying out a forensic analysis of the trail he left in N.S.A. computer systems, trying to determine what he had access to as a systems administrator for Booz Allen Hamilton, a United States government contractor, and what he may have downloaded, officials said. 

The South China Morning Post reported Monday night on its Web site that in an interview, Mr. Snowden said he had specifically sought the job at Booz Allen so he could collect information about the N.S.A.'s secret surveillance programs to release to news outlets. 

Glenn Greenwald, a columnist for The Guardian, has said Mr. Snowden gave him thousands of documents, only a tiny fraction of which were published. Many may be of limited public interest, but they could be of great value to a foreign intelligence service, which could get a more complete idea of the security agency’s technical abilities and how to evade its net, officials said.