Palestinian Prisoners Affairs Minister Hisham Abdelrazaq said on Thursday Abbas wants Israel to first agree in principle to the release of all the estimated 6,000 prisoners before drawing up a schedule for their release.
"If America succeeds, there will be progress in the peace process but if they do not, the political process could be destroyed," the minister said.
Abdelrazeq was speaking ahead of a rally in Gaza City where about 500 members of resistance groups such as Hamas and Islamic Jihad, as well as Fatah, called for the release of all of their members held in Israeli jails.
An Israeli ministerial commission Wednesday ruled out the release of any members of those groups - a move Palestinians said was a "severe blow" to the three-month truce.
"The decision to refuse to release members of Hamas and Islamic Jihad is a clear violation of the ceasefire agreement. It shows Israel refuses to fulfill the pledges it has made to Abbas and the international community," Jihad leader Sheikh Khaledal-Battash said.
Abbas, who arrived in Washington on Wednesday on his first official visit to the US, is also expected to ask Bush to persuade Israel to stop construction of the wall.
Israel acknowledges a rift is emerging with Washington over the issue and Prime Minister Ariel Sharon will try in his own White House talks on 29 July to convince Bush of the need to press on with the wall for "security reasons".
Bush's National Security Advisor Condoleezza Rice criticised the contours of the wall on a visit to the region at the end of last month.
She told Sharon the fence was seen by Palestinians as an attempt by Israel to set in stone the borders of a future Palestinian state. Under the US-backed roadmap for peace, the borders must be the subject of negotiations.
The high concrete wall - with a total length of 800 to 900 kilometres - has been described as a disaster by the Palestinians and human rights organisations around the world.
It deprives them of up to 20 percent of the surface area of the West Bank including some of its most fertile lands.
"The settlements will also be discussed during the Abbas-Bush meeting," Palestinian Information Minister Nabil Amr told Aljazeera.
"When we talk about the wall we are not only talking about 20 percent of confiscated land but the Jewish settlements across the West Bank," he added. "If you want to establish peace, you cannot seize the land of others."
The roadmap calls for a freeze on all Jewish settlement activity but interior ministry figures released Thursday showed the number of settlers living in the West Bank and Gaza has risen by 5,400 in the past year to a record 231,443.