WASHINGTON — The nation’s top spymaster said on Tuesday that the White House had long been aware in general terms of the National Security Agency’s overseas eavesdropping, stoutly defending the agency’s intelligence-gathering methods and suggesting possible divisions within the Obama administration.

The official, James R. Clapper Jr., the director of national intelligence, testified before the House Intelligence Committee that the N.S.A. had kept senior officials in the National Security Council informed of surveillance it was conducting in foreign countries. He did not specifically say whether President Obama was told of these spying efforts, but he appeared to challenge assertions in recent days that the White House had been in the dark about some of the agency’s practices.

Mr. Clapper and the agency’s director, Gen. Keith B. Alexander, vigorously rejected suggestions that the agency was a rogue institution, trawling for information on ordinary citizens and leaders of America’s closest allies, without the knowledge of its Washington overseers.

Their testimony came amid mounting questions about how the N.S.A. collects information overseas, with Republicans and Democrats calling for a congressional review, lawmakers introducing a bill that would curb its activities and Mr. Obama poised to impose his own constraints, particularly on monitoring the leaders of friendly nations. At the same time, current and former American intelligence officials say there is a growing sense of anger with the White House for what they see as attempts to pin the blame for the controversy squarely on them.