Blair aimed to capitalize on new optimism in the region in the wake of Yasser Arafat's death and Israel's moves to pull out of the Gaza Strip.
However, Blair said the Palestinians must crack down on militants before new peace efforts can begin, including a revival of the internationally-backed "road map" peace plan.
"There is not going to be any successful negotiation or peace without an end to terrorism," Blair said during a news conference with Sharon. "The absence of terrorism then can create the situation in which a proper negotiated settlement can take place."
Mahmoud Abbas, the interim Palestinian leader who is running to replace Arafat in Jan. 9 elections, has unsuccessfully tried to negotiate a cease-fire with Palestinian militant groups. Militants in the Gaza Strip have launched repeated mortar and rocket attacks in recent weeks on Israeli settlements and military bases.
Israeli troops raided the Khan Younis refugee camp in southern Gaza early Wednesday in its second offensive in the past week to stop the mortar attacks. The raid Wednesday killed a Palestinian militant, according to Israeli and Palestinian officials.
Sharon said that if there is a "full cessation of terror, hostilities and incitement, the door will be open for the road map, which will change, I believe, the life of the Israelis, the Palestinians and change the situation in the region."
But so far the Palestinian's have made no moves to stop the attacks, he said.
"We don't see even the slightest step taken by the Palestinians. I understand there are elections now ... but they are not doing even the slightest effort," he said in his first openly critical remarks about Abbas since Arafat's death.
"The viability has to be that of a state that is democratic, that is not giving any succor or help to terrorism," said Blair.
Sharon said Israel will coordinate its planned withdrawal from the Gaza Strip with the Palestinians, reports CBS News Correspondent Robert Berger. Peace talks are expected to resume after Palestinian elections next month
Blair said his proposed London meeting would have narrow goals, focusing on strengthening and reforming the Palestinian administration, its security forces and financial system.
Such reforms would allow the Palestinians to capitalize on Israel's Gaza pullout and "become a real partner for peace with Israel," said Blair, who was later to meet with Palestinian officials.
The Palestinians had hoped Blair would propose a major international peace conference dealing with the thorny issues that have stymied past peace efforts.
"I think the aim is not only to hold an economic conference or to strengthen the Palestinian Authority, these are minor things. The main aim is we need to find out if there is a peace process or not," Palestinian Prime Minister Ahmed Qureia said Wednesday.
Israel said the conference should deal only with reforms in the Palestinian Authority and new donor aid for the Palestinians, and said it had no plans to attend.
Blair appeared to agree with Israel, saying that major peace conferences will likely have to wait until after the Gaza pullout, scheduled to begin in July.
The settlers in Gaza said earlier this week they planned to resist Israel's efforts to evacuate them.
As part of the new wave of diplomacy, Italian Foreign Minister Gianfranco Fini met with Abbas on Wednesday and endorsed the Palestinian leader's candidacy, saying he could lead the Palestinians to a prosperous future and statehood.
"If Mahmoud Abbas is elected, and I hope he is, we will have good reason to be pleased," Fini told a news conference in Ramallah before laying a wreath on Arafat's tomb. Arafat died Nov. 11.
Abbas, a pragmatist who has the tacit support of Israel and the United States, is the front-runner in the elections.
Meanwhile Wednesday, Israel sent tanks and bulldozers back into Khan Younis, just three days after ending an operation in response to rocket and mortar fire by Palestinian militants.
Israeli forces in the camp killed a Palestinian militant, Palestinian security forces said. The Israeli military said soldiers shot an armed Palestinian in the western part of the camp.
Israeli bulldozers also destroyed several homes in the camp. About 20 Palestinians demonstrated in the camp carrying Palestinian and British flags and demanding Blair stop the demolitions.
Israel's earlier raid into the camp killed 11 Palestinians, most of them militants. But the rocket fire resumed after the army pulled out of the camp Sunday. In the last two days, mortar shells hit a synagogue and a kindergarten in nearby Jewish settlements.
The military said the current push would last about two days, and buildings used as cover by militants were being destroyed. Some exchanges of gunfire were heard, but there were no reports of casualties.
In another initiative Tuesday, James Wolfensohn, the president of the World Bank, pushed for Palestinian economic reforms and the lifting of Israeli travel restrictions in the West Bank in exchange for an additional US$500 million in desperately needed aid to the Palestinians.