WASHINGTON — Senators are questioning top Obama administration officials about the National Security Agency’s surveillance programs for the first time since the House narrowly rejected a proposal last week to effectively shut down the NSA’s secret collection of hundreds of millions of Americans’ phone records.

The Senate Judiciary Committee hearing Wednesday will include testimony from the No. 2 officials at the Justice Department, FBI and NSA, plus the top lawyer for the Office of the Director of National Intelligence. It will also include testimony from James G. Carr, a senior federal judge who previously served on the secretive Foreign Intelligence Surveillance Court and who recently urged Congress to give such judges more discretion and authority to appoint lawyers to serve the interests of the public.

Carr has said to do otherwise “puts basic constitutional protections at risk and creates doubts about the legitimacy of the court’s work and the independence and integrity of its judges.”

The government acknowledged last week in a letter to Congress that there have been an unspecified number of “compliance problems” in following the rules put in place governing the secret collection of Americans’ phone records. The director of national intelligence, James Clapper, said no intentional or bad-faith rules violations were found.

Since the NSA surveillance became public two months ago, the chairman of the Judiciary Committee, Sen. Patrick Leahy, D-Vt., has introduced legislation that would allow the government to obtain phone records only when it can establish that the information is relevant to an authorized investigation and is linked to a foreign terrorist group or foreign power. Leahy’s bill would enhance oversight by expanding reporting requirements to Congress and would add further court review of surveillance programs. The measure also would add a new sunset provision for national security letters, which are issued by government agencies such as the FBI to gather information such as phone numbers dialed or sender or recipient email addresses.

Former NSA systems analyst Edward Snowden leaked documents revealing the NSA’s phone records program. Snowden also leaked details of a second NSA program called PRISM, which forces major Internet firms to turn over detailed contents of communications such as emails, video chats and pictures.

Last year, the Judiciary Committee approved Leahy’s measure to bolster limits on surveillance. Ultimately, Congress passed a long-term extension of intelligence programs without any new reforms.

Last week’s House vote of 217-205 was significant not only because of the narrowness of the victory for the Obama administration, but because it created unusual political coalitions. Libertarian-leaning conservatives and liberal Democrats pressed for change against the Republican establishment and Congress’ national security experts.

Backing the NSA program were 134 Republicans and 83 Democrats, including House Speaker John Boehner, R-Ohio, who typically does not vote, and Democratic leader Nancy Pelosi. Rejecting the administration’s last-minute pleas to spare the surveillance operation were 94 Republicans and 111 Democrats.