Jerusalem: Israeli Prime Minister Benjamin Netanyahu on Friday raised the possibility that some Jewish settlements would remain under Palestinian sovereignty if the two sides struck a peace deal.

"It is clear that some of the settlements will not be part of a (peace) deal," Netanyahu, wrapping up a visit to the United States, told Israeli television.

"I will not abandon anyone. I will not leave any Israeli unprotected," he added when asked if some West Bank areas with settlements would form part of a future Palestinian state.

The prime minister reiterated that peace with the Palestinians hinged on their recognition of Israel as a Jewish state and ruled out concessions on annexed east Jerusalem where the Palestinians want to set up their future capital.

Netanyahu met Monday with US President Barack Obama who told him that Israel needed to take tough decisions if peace talks with the Palestinians were to advance.

Obama is due to meet Palestinian leader Mahmud Abbas on March 17 at the White House.

US Secretary of State John Kerry has been struggling to get Israel and the Palestinians to agree a framework for extending direct peace talks beyond an April 29 deadline.

But Israel and the Palestinians remain divided on all the major issues, including borders, security, settlements, Jerusalem and Palestinian refugees.