TEL AVIV — President Mahmoud Abbas of the Palestinian Authority said in an interview shown Tuesday that he could accept an Israeli military presence in the West Bank for a three-year transition period as part of a peace deal. But Mr. Abbas said “whoever proposes 10 or 15 years for a transition” was not serious about an agreement.

The question of who should be responsible for security, particularly in the Jordan Valley, and for how long, has been central in the American-brokered peace talks between the Israelis and the Palestinians that started this summer.

Israel has long insisted that it can depend only on its own soldiers, not an international force, with some leaders suggesting they might stay for 40 years or more. Palestinian officials have said they could not tolerate even a single Israeli soldier patrolling their future state, though they have acknowledged that some transition period would most likely be required.

“We say that a transition period not exceed three years, during which Israel will withdraw gradually,” Mr. Abbas said in a videotaped interview shown at an Israeli security conference here, in his most specific recent public comments on the subject. “We are willing to allow a third party to take Israel’s place during and after a withdrawal in order to soothe our concerns and Israel’s.” He suggested NATO as “the suitable party.”