Speaking after a meeting between Mr Abbas and Hosni Mubarak, the Egyptian president, Omar Suleiman - Egypt's lead negotiator with the Palestinians - said that Mr Abbas was also demanding that Hamas, which won a stunning victory in parliamentary elections, accept agreements which the Palestinians signed with Israel.
Egypt's version of Mr Abbas's position was disputed to an extent by Palestinian Authority officials and dismissed by Hamas and may be an attempt by Egypt to crank up the pressure on Hamas to modify its position before it takes power.
Refusing to allow Hamas to form a government could lead to further conflict with Mr Abbas's Fatah party. In the Gaza Strip yesterday, an explosion blew out the walls of the home of a leading Fatah official, Suleiman Abu Mutlak, which he claimed was a Hamas assassination attempt.
Hamas's charter, which its leaders are refusing to amend, calls for Israel's destruction and the movement has led a suicide bombing campaign responsible for the deaths of hundreds of Israelis.
This has led foreign donors of aid such as the United States and the EU, which together give more than 500 million a year to the Palestinian Authority, to threaten to withdraw funds.
The first step towards a major financial crisis came yesterday when Israel made good on a threat to suspend the transfer of about 30 million in customs payments which it collects every month on behalf of the authority. The money is used to pay many of the authority's 135,000 employees. Saudi Arabia and Qatar promised to give 18.5 million to help keep up payments.
Farhat As'ad, a Hamas spokesman in the West Bank, said Israel was "opening the gates of hell" by suspending the money transfers and that it would lead to greater extremism and fuel violence.
Responding to the claims by Mr Suleiman, Palestinian Authority officials in Ramallah said yesterday that formal recognition of Israel would not be a prerequisite for Hamas forming a government.
However, they said the new government would have to adhere to the 1993 Oslo self-rule agreement with Israel and other international commitments of the Palestinian Authority, including the United States-backed "road map" peace plan, which lays out a two-state solution to the crisis.
But Mr Suleiman said in remarks first reported by Israeli officials: "Hamas has to be committed to three issues: first, to stop violence, this should be its doctrine; second, to be committed to all the agreements signed with Israel and third, to recognise the existence of Israel."
Using Mr Abbas's nickname, he added: "If they don't do this, Abu Mazen will not ask them to form the government."
Mr As'ad dismissed the remarks as "incorrect" while Musa Abu Marzouk, a senior Hamas official, flatly ruled out any recognition of Israel.
However, he said that Hamas would be interested in extending a one-year ceasefire agreed with Mr Abbas.
In recent years, Egypt has maintained good relations with the Hamas movement in order to exercise leverage over it.
Yesterday, a delegation of Hamas leaders was headed for talks in Cairo with Egyptian officials. The Israeli foreign minister, Tzipi Livne, also held talks with Mr Mubarak in Cairo yesterday to discuss policy towards Hamas.
Abu Marzouk, the senior Hamas leader, rejected calls by George Bush, the US president, for Hamas to disarm and recognise Israel, saying the movement would not change its principles.
"These conditions cannot be accepted and the US president should accept the reality, because the Palestinian people have exercised their democratic choice with mechanisms that are basically western and they chose Hamas," he said.
Mr Bush "should deal with Hamas as it is", he said. But, he added: "We understand that they [western nations] need a quiet region, without conflicts and we know it is possible to attain this goal. Truce is one of the projects through which we could deal with [this].
"I believe this would placate everybody if they understand Hamas's stand and talk to Hamas on these grounds."
Ghassan Khatib, the Palestinian Authority's labour minister, said in response to Mr Suleiman's comments that Mr Abbas was not demanding that Hamas should formally recognise Israel.
Rather, he said, Mr Abbas would demand that a Hamas government make clear that it respects existing treaties.
"President Abbas will ask Hamas to form the government, but within the norms of any government, namely that it has to continue to respect the commitments of the state to the external parties," Mr Khatib said.
"He can say that he won't ask Hamas to form a government until it abides by the commitments of the Palestinian Authority.
"The president has the right constitutionally to impose on any party that they have to take into consideration the Palestinian international commitments."
If a Hamas cabinet refuses to uphold authority commitments "then we are in a deadlock", Mr Khatib said.
Hamas has consistently rejected the Oslo Agreement as a sell-out of Palestinian rights.
It is thought that both the failure of Oslo and Mr Abbas's path of negotiations to bring tangible improvements to Palestinian life contributed greatly to Hamas's electoral rout of Mr Abbas's Fatah movement last week.
Hamas's electoral platform specifies that it continues to claim rights not only to all of the West Bank and Gaza Strip but also to the territory that comprises Israel within its 1967 borders.
Reacting to Israel's freezing of funds to the Palestinian Authority, Maher Masri, the authority's former economics minister, said he hoped the Israelis would reconsider. "This is a violation of our signed agreements with Israel. You don't treat a wrong by performing another wrong," he said.
He claimed that the authority would now be able to pay only part of the salaries of its employees, and that more than a million people would be directly affected.
"This money is crucial to the generation of economic activity and there will be a ripple effect," Mr Masri said.