By David Brunnstrom

BRUSSELS, March 25 (Reuters) - Palestinians and Israelis must try to improve living conditions in the West Bank and Gaza Strip to keep the peace process alive ahead of a visit by U.S. President George W. Bush in May, peace envoy Tony Blair said on Tuesday.

Blair also told the European Parliament that progress in the peace talks was crucial to build Palestinian confidence in the negotiations and to show Israelis that Palestinians could take charge of security, and called for a new strategy on dealing with the Hamas-run Gaza Strip.

"We are approaching the crunch time for this stage of this process," said the former British prime minister, now envoy for the Quartet of Middle East peace brokers -- the United States, the European Union, Russia and the United Nations.

"President Bush will go back to Israel at the beginning of May," he said. "I think it's got to be fairly clear by then that we are in a different and better position than we are today."

Blair said Palestinians and Israelis need to agree on projects to ease the impact of the Israeli occupation, including establishing industrial parks, infrastructure projects and an easing of access and movement restrictions.

Defence Minister Ehud Barak said on Monday Israel will try to ease some travel restrictions within the occupied West Bank but is not ready to commit to removing checkpoints that stifle movement, saying they were needed for security.

Blair said Israel must work with the Palestinian Authority and the international community to ensure that goods and humanitarian supplies reach the Gaza Strip, where most of the 1.5 million Palestinians there live on handouts.

"If we've learned anything from the past few months it is that the present strategy in Gaza is not working," Blair said, referring to the Israeli blockade on the territory.

"We need a strategy that isolates the extremists and helps the people and at the moment if we are not careful we've got the opposite, which is that we are isolating the people and helping the extremists, and that is not intelligent."

Blair said peace negotiations between the Palestinians and the Israelis needed "a significant change in the context, the realities on the ground, to get to fruition".

"It is possible to get this resolved but we need to be aware of the fact that we are racing against time," he said, referring to the talks, which had made virtually no progress since they were re-launched in November.

France's Europe Minister Jean-Pierre Jouyet, called for "concrete gestures" from Israel that were visible on the ground.

"Without this we risk seeking the position of the moderates weakened and that of the extremists reinforced," he said, terming Israeli army military operations in the Gaza Strip settlement building in the West Bank counter-productive.

He also endorsed a reconciliation deal reached in Yemen on Sunday between Hamas and the secular Fatah group headed by Palestinian President Mahmoud Abbas.

The rival Palestinian factions Fatah and Hamas promised to revive direct talks after months of hostilities, but differences remained over the future of the Gaza Strip and West Bank. (Reporting by David Brunnstrom; editing by Sami Aboudi)

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