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 Moscow’s Sheremetyevo airport, did not board the flight for Havana he was said to have booked, and he made no public appearance or statement.

American officials said they believed he was still in Moscow, but it was unclear whether his failure to continue on to Cuba, Ecuador or elsewhere was a sign that Russia was considering handing him over to the United States, sheltering him itself, planning to allow him to leave later or trying to extract information from him before deciding. The United States and Russia do not have an extradition treaty.

Nikolay N. Zakharov, a spokesman for Russia’s Federal Security Service, or F.S.B., declined to say if intelligence officials had met with Mr. Snowden, nor would he say if they had sought to examine any secret files he was said to be carrying. “On this question, we will not comment,” Mr. Zakharov said.