Israel freed 500 prisoners in February as part of understandings reached with Abbas at the 8 February summit when the two sides declared a ceasefire.
But Sharon froze the release of 400 more prisoners, citing Palestinian inaction in disarming other groups.
Palestinians for their part accused Israel of delay tactics and backtracking on the agreement.
The prisoner releases were intended to boost Abbas among the Palestinian public, who see the detainees as freedom fighters against Israeli occupation.
Abbas left to Washington on Tuesday with the hope of pressing Bush to "stick seriously" to the road map and avoid promises to Israel about the outcome.
His trip to the White House has symbolic significance as it will be the first since 2000, when earlier peace talks aimed at Palestinian statehood collapsed into bloodshed for which Washington often blamed his predecessor, Yasser Arafat.
Abbas said he would tout to Bush his achievements since being elected in January, including an uneasy calm he agreed to with Palestinian groups and a start to urgent security reforms - both preconditions of the US-devised "road map".
He would also urge Bush to make Israel uphold its obligations in the plan by, for instance, linking the pullout of 8500 Jewish settlers from Gaza with a freeze on the growth of the much larger settlements in the occupied West Bank.
But Sharon, in his address to American Jews, hammered home his basic position that there could be no progress on the US-backed road map until Abbas takes action against Palestinian groups.
"Until now the terrorist activities have not ceased ... and there is no real prevention of terrorist actions," Sharon told a cheering crowd at the annual AIPAC convention, capping a three-day visit with US Jewish leaders.
Sharon says integration of other
groups will hinder the road map
In a speech to the most powerful US pro-Israel group, the American-Israel Public Affairs Committee, Sharon also proposed coordinating with the Palestinian Authority Israel's planned mid-August pullback from the Gaza Strip.
He said such cooperation would enable Israel and the Palestinians "to embark on a new era of trust and build our relations with the Palestinian Authority".
In a gesture to Abbas, who will meet US President George Bush on Thursday, Sharon said he would seek the approval of his cabinet for the release of 400 Palestinian prisoners after he returns home later this week.
His address was interrupted by a heckler opposed to the pullback.
She shouted "I live in Gush Katif", a reference to the main Jewish settlement bloc in Gaza, and "it's an expulsion, an expulsion", before being hustled out by security.
Sharon said integrating Palestinian groups into the Palestinian political system, a reference to Hamas's plans to run in the 17 July parliamentary election, would only strengthen Palestinian factions and hinder progress on the road map.
It charts mutual steps towards the establishment of a Palestinian state in the West Bank and Gaza.
"We will do our utmost to cooperate ... as long as we do not risk our security - that is the
Israeli Prime Minister
"We will do our utmost to cooperate with the new Palestinian leadership and will take the needed measures to help Chairman Abbas," he said, adding the proviso "as long as we do not risk our security - that is the red line".
Hunger strike ends
Meanwhile, 13 Palestinian political detainees in the Palestinian Authority prison in Jericho have decided to end their hunger strike after receiving promises from members of the Palestine Legislative Council to resolve their case.
Dozens of Tulkarim residents staged a street protest in solidarity with the detainees. The raised posters demanded the release of all political detainees.
The detainees, who belong to the military wings of the Islamic Jihad and Fatah movements, began a hunger strike five days ago in protest against their detention without trial.
In a separate development, an Egyptian delegation resumed mediation efforts with the main Palestinian factions in Gaza.
Egyptian intelligence officials are
trying to negotiate a durable deal
On Tuesday, the Egyptian team of intelligence and security officials held meetings in Gaza City with officials of a number of Palestinian factions as part of Cairo's initiative to put the Palestinian house in order and help cement the Israeli-Palestinian truce.
The Egyptians met representatives of the Islamic Jihad, the Popular Liberation Front and the Democratic Liberation Front.
For its part, the Islamic Jihad reiterated its readiness to cooperate with the Egyptian delegation to put an end to tensions between Hamas and Fatah over the outcome of the recent municipal elections.