WASHINGTON — 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.