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 on Thursday, senators pressed John O. Brennan, President Obama’s nominee for director of the CIA, 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 Senate Intelligence Committee’s chairwoman, Senator Dianne Feinstein, Democrat of California, said she would review proposals to create a new 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 US soil.