Jericho, West Bank ? Secretary of State Colin Powell pored over detailed territorial maps with the leaders of Israel and the Palestinian Authority in separate meetings Friday, praising the Israelis for efforts toward an eventual peace settlement and urging speed on the Palestinians.

In return, he was assured the Palestinians would move quickly to take over from Israeli forces responsibility for security on the Gaza Strip.

Prime Minister Ariel Sharon said after his meeting with Powell that Israel would “exhaust every avenue” in the search for peace. He cautioned, however, that fulfillment of the U.S.-backed “road map” was contingent on the Palestinians’ curbing terrorism.

“The Palestinian Authority must fight terror organizations, it must disarm them, it must make sure that their infrastructure no longer exists,” Sharon said.

Powell said he was encouraged by the steps Israel had taken in recent weeks, including release of some Palestinian prisoners and dismantling of structures in the occupied territories that settlers built without government authorization.

Powell’s praise for the Israelis contrasted with his subsequent admonition to Palestinian leaders.

“When I meet with Prime Minister Abbas this afternoon, I will urge him to move quickly, very quickly, to implement security reforms and to come forward with specific plans to take responsibility for security in Gaza and Bethlehem,” Powell said.

On Gaza, at least, Powell received assurances he was seeking from Mahmoud Abbas.

“The Palestinians told us they want to move on Gaza,” a senior State Department official said.

With an assist from U.S. special envoy John Wolf, Israel and the Palestinians have been discussing the withdrawal of Israeli forces and their replacement by Palestinians.