(Adds Israeli reaction, previously NABLUS)

By Mohammed Assadi

RAMALLAH, West Bank, Feb 7 (Reuters) - International Middle East envoy Tony Blair said on Thursday Palestinian security forces had significantly improved and were starting to carry out their part in a long-stalled "road map" peace plan.

The former British prime minister urged Israel to respond by easing travel and trade restrictions for Palestinians in the occupied 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 Israeli 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 recognise 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 to the south in Ramallah, he said: "The Palestinian side have improved significantly their security capability."

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

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

"We agree that the PA (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, who serves as special envoy to the Quartet of Middle East mediators, will have on the road map judging process, though he is close to Bush.

Abbas, whose authority is limited to the occupied West Bank since Hamas Islamists 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. (Additional reporting by Adam Entous in Jerusalem and Haitham Tamimi in Hebron; Writing by Adam Entous; Editing by Michael Winfrey)

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