US Middle East envoy George Mitchell met with Mubarak earlier and then held talks with Mussa, who later told reporters the Palestinians could not move automatically from the indirect talks to face-to-face negotiations.
"We cannot automatically move from one negotiation to another without written guarantees," said Mussa.
"I felt the Palestinian president was committed to the decisions of the ministerial council that the automatic transition from indirect to direct negotiations is not feasible," he said about his meeting with Abbas on Saturday.
The Arab League backed the indirect talks in March but supported their suspension after Israel said it would build more Jewish homes in annexed east Jerusalem.
It backed the talks again in May after the Palestinians said they received unspecified guarantees, but said direct negotiations would come only after a complete end to settlement building in occupied Palestinian lands.
Netanyahu had told reporters before flying to Cairo that he would discuss the prospects for direct talks with Mubarak.
Foreign Minister Ahmed Abul Gheit said Mubarak told his visitors "Israel had to take a strong, strategic move that would deepen the Palestinians' trust towards Israel's intentions, and consequently we could encourage a move to direct negotiations," Egypt's official MENA news agency reported.
The Palestinian leadership restated the conditions for the direct talks, suspended since Israel's offensive on Gaza in December 2008, after a meeting between the US envoy and Abbas in the West Bank town of Ramallah on Saturday.
Senior Palestinian official Yasser Abed Rabbo called for greater clarity from Washington about its position on new negotiations, insisting the Palestinians wanted to address the core issues of the Middle East conflict.
"The three-hour meeting between Abbas and Mitchell was important but there are several issues, most important among them the settlements and the situation in Jerusalem, that need more clarity," Abed Rabbo told reporters.
The Palestinians have demanded a complete freeze on Israeli settlement expansion ahead of direct talks and have accused Israel of undermining the process by approving new settler homes in mainly Arab east Jerusalem, which they want as the capital of their promised state.
Earlier this month, during a visit to Washington by Netanyahu, Obama said he hoped to see direct talks begin before a partial Israeli moratorium on the expansion of Jewish settlements in the occupied West Bank ends in September.
In recent weeks, Abbas had appeared to back away from his previous demand for a full settlement freeze as a condition for opening direct talks, instead insisting on "progress" on the issue of borders and security.
In an interview published on Saturday, he said he would meet Netanyahu if Israel agreed in principle to a Palestinian state based on the borders before Israel's occupation of the West Bank during the 1967 war, with equal land swaps and the presence of an international security force.
"Israel must accept that the Palestinian territory in question be that of the 1967 borders and with the presence of a third party," he told Jordan's Al-Ghad newspaper, referring to Gaza and the West Bank, including east Jerusalem.
"This will push us to embark on direct negotiations," Abbas said.
In an indication of the domestic pressure facing Abbas, his own Fatah party on Thursday told him not to join direct talks with Israel without showing progress in the indirect talks.
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