The Quartet's Middle East envoy Tony Blair said Thursday that Palestinian security forces had significantly improved and were starting to carry out their part in the long-stalled "road map" peace plan.

The former British prime minister, now the envoy for the Quartet of Middle East peace mediators which include the European Union, the United States, Russia and the United Nations, urged Israel to respond by easing travel and trade restrictions imposed on the Palestinians in the West Bank.

The U.S. government will assess and judge whether Israel and the Palestinians are meeting their obligations under the 2003 road map as part of a push for a Palestinian statehood agreement before U.S. President George W. Bush leaves office next January.

Statehood could hinge on those assessments because Prime Minister Ehud Olmert has vowed not to implement any future peace agreements until Palestinian President Mahmoud Abbas meets his road map obligation to crack down on militants.

"I think it is important to recognize that what has happened here in Nablus over these past few months is, of course, precisely what phase one of the 'road map' asks for," Blair said during a visit to the West Bank city.

Earlier Thursday, during a visit south of Ramallah, he said: "The Palestinian side has improved significantly their security capability."

Israel has yet to fulfill its own road map commitments to halt Jewish settlement activity and to uproot outposts built without government authorization in the West Bank.

Israeli officials said the Palestinians had a long way to go before they would meet their security obligations, citing a suicide bombing this week in southern Israel.

"We agree that the Palestinian Authority has started to move on implementing obligations under the 'road map', but obviously much more still has to be done," Olmert's spokesman, Mark Regev, said.

It is unclear what direct influence Blair will have on the road map judging process, though he is close to Bush.

Abbas, whose authority has been limited to the West Bank since Hamas seized the Gaza Strip last June, started a security campaign late last year in Nablus, seizing weapons and arresting criminals as well as some militants.

Citing what he called progress by the Palestinians, Blair said Israel "in time" should remove checkpoints and other restrictions on Palestinian travel and trade.

"The single most important thing for the economy is, bit by bit, to lift the occupation," he said. But, he added: "For all sorts of reasons, we know this will take time."

Hamas's armed wing claimed responsibility for Monday's suicide bombing, which killed an Israeli woman. The group said the bomber and a second attacker, killed at the scene by police, came from the southern West Bank city of Hebron.