MOSCOW — President Vladimir V. Putin told an audience of students on Monday that the United States had effectively trapped Edward J. Snowden, the fugitive former intelligence contractor, on Russian territory by frightening countries that otherwise might have accepted him. When Mr. Putin insisted that Russia did not want Mr. Snowden to cause damage to the United States, the students laughed out loud.

Mr. Putin made the remarks on Hogland Island in the Gulf of Finland, where he was reviewing projects of the Russian Geographical Society. He spoke about Mr. Snowden, who announced on Friday that he would formally request asylum in Russia, during a meeting with student researchers who were attending an archaeological camp on the island.

Russian officials said Monday that they still had not yet received an application from Mr. Snowden, and Mr. Putin did not say outright whether he would grant a request from him. But the president clearly signaled that it remained a possibility.

Mr. Snowden arrived at Sheremetyevo Airport outside Moscow on a flight from Hong Kong on June 23, and he has been there ever since, living in the transit zone of the airport with the consent of the Kremlin and apparently with some support from the Russian authorities. On Friday, Mr. Snowden met at the airport with lawyers, Russian officials and representatives of human rights organizations.