(Repeats to remove repetition in paragraphs 4,5)

By Axel Bugge and Sue Pleming

LISBON, July 19 (Reuters) - The Quartet of Middle East mediators threw its weight on Thursday behind a U.S. plan to reinvigorate Israeli-Palestinian peacemaking and pledged support for all Palestinians, including those in Gaza.

The Quartet met for the first time since Hamas Islamists seized control of the Gaza Strip from U.S.-backed President Mahmoud Abbas's forces last month, effectively dividing Palestinians between Gaza and the West Bank.

The meeting of top diplomats from the United States, Russia, the European Union and the United Nations was also the first with former British Prime Minister Tony Blair as its envoy. Delegates hope he will help kick-start Middle East peace moves with passion and commitment.

"Just imagine for a moment if this process were moving forward again, just think how much hope there would be," Blair told reporters after the meeting.

"I hope I can offer something in bringing about a solution to this issue that is of such fundamental importance to the world," Blair said.

Blair will travel to the Middle East and he will report back to the Quartet on his strategy of economic and institutional reforms for the Palestinians in September, a statement from the meeting said.

U.S. President George W. Bush announced this week he intends to hold a Middle East peace conference later in the year, probably in the United States. U.S. Secretary of State Condoleezza Rice soon will visit the Middle East to try to boost support for the conference.

BUSH STATEMENT WELCOME

"The Quartet welcomed President Bush's July 16 statement renewing U.S. commitment to a negotiated two-state solution," U.N. Secretary-General Ban Ki-moon said, reading from the statement issued by the Quartet.

"What you have heard today is a recommitment of the international community to rapidly pursue policies that can lead to that outcome (a two-state solution)," Rice said.

It is years since Israel and the Palestinians last discussed issues at the root of the conflict -- final borders of a Palestinian state, the return of refugees and the status of Jerusalem.

The Quartet pledged to go on supporting Gaza Palestinians. Aid agencies have urged an easing of an effective trade embargo on Gaza, where poverty is increasing.

"We are going to continue helping the Palestinian people that are in Gaza," European Union foreign policy chief Javier Solana said.

"The Quartet expressed its deep concern over the humanitarian conditions in Gaza and agreed on the importance of continued emergency and humanitarian assistance," the Quartet statement said.

The statement made no mention of Hamas, which controls Gaza. The United States maintains a boycott against Hamas, which it classifies as a "terrorist" organisation.

Blair on Monday will visit Israel and the West Bank, where Abbas's Fatah is in control. It will be his first visit since he became the Quartet's envoy.

Israeli Prime Minister Ehud Olmert met Abbas this week but Israel again ruled out negotiations for now on the borders of a future Palestinian state. To help Abbas, Israel decided to release 256 Palestinian prisoners. (Additional reporting by Henrique Almeida)

AlertNet news is provided by