Engaging a high-ranking Obama administration official for the first time in an extensive public discussion of the use of drones for targeted killing, members of the Senate Intelligence Committee on Thursday pressed John O. Brennan, President Obama’s nominee for director of the Central Intelligence Agency, about the secrecy of the strikes, their legal basis and the reported backlash they have produced in Pakistan and Yemen. Adding a new element to the roiling debate, the committee’s chairwoman, Senator Dianne Feinstein, Democrat of California, said she would review proposals to create a court to oversee targeted killings. She gave no details but said such a court would be analogous to the Foreign Intelligence Surveillance Court, which oversees eavesdropping on American soil. Mr. Brennan was noncommittal, noting that lethal operations are generally the sole responsibility of the executive branch. But he said the administration had "wrestled with” the concept of such a court and called the idea "certainly worthy of discussion.” On the same day two other administration officials, Defense Secretary Leon E. Panetta, and Gen. Martin E. Dempsey, chairman of the Joint Chiefs of Staff, acknowledged in testimony before the Senate Armed Services Committee that a plan they had supported to arm Syrian rebels had been rejected by the White House, the notably aggressive questioning Mr. Brennan received seemed to underscore the increased scrutiny Mr. Obama’s national security policies are facing as he begins his second term. Mr. Brennan, 57, a 25-year C.I.A. veteran who has spent the last four years as the administration’s senior counterterrorism official, also faced intense questioning about whether he was responsible for leaks of classified information, and whether he had been candid about his involvement in the agency’s interrogation program under President George W. Bush. But the senators repeatedly returned to the targeted killings Mr. Brennan has helped direct over the last four years. The hearing came three days after the leak of a Justice Department document explaining the legal rationale for the killing of American citizens who join Al Qaeda. On the eve of Mr. Brennan’s hearing, the White House gave in to pressure from lawmakers and said the Senate and House Intelligence Committees could see the full classified legal memorandum justifying the killing of Anwar al-Awlaki, an American-born cleric who joined Al Qaeda in Yemen and was killed in Yemen in a C.I.A. drone strike in September 2011. Ms. Feinstein expressed frustration at the committee’s difficulty in getting information about the targeted killing program. She said that while senators were allowed to view two legal memos, they were still seeking eight others, and committee staff members were still prohibited from reading the classified documents.