"We cannot say that there has been an agreement but the discussions have not ended yet and they are set to resume tomorrow," Abbas's spokesman, Nabil Abu Rudeina, told reporters after the nearly three-hour meeting in Gaza City.
"Some issues need further discussions and we hope to be able to resume the talks tomorrow or the day after," he said.
"There is an agreement on the necessity to form a government of national competence. But we have to agree on a few issues in order to reach a final agreement."
Lawmaker Mustafa Barghuti, who has been mediating between the leaders of the two rival Palestinian factions, said: "We're moving, I hope, on the right track."
Abbas has tried but failed for months to persuade the ruling Hamas party to accept a moderate political platform acceptable to the international community in order to lift a crushing economic and political boycott.
The embattled president is the only Palestinian partner for the West, which has cold-shouldered Hamas since it took office last March.
Monday's meeting was the first face-to-face meeting between the two rival leaders since mid-September and comes with Israel waging a six-day operation in the northern Gaza Strip in which 55 Palestinians have been killed and more than 200 wounded.
Abbas is trying to persuade Hamas to soften its stance on key demands that have blocked agreement for months -- namely to recognise Israel, renounce violence and abide by past peace deals.
Earlier, sources in the Palestinian presidency said communications and technology minister Jamal al-Khodari, an independent seen as close to but not a member of Hamas, would head up a new unity government.
Khodari refused to comment other than confirming "an agreement within Hamas on the name of the prime minister who will lead the national unity government".
Following Monday's talks, Barghuti said only that the name of the future premier "was brought up".
Hamas has always insisted that the incoming premier and make-up of any unity cabinet take into account the results of last January's general election which the movement won by a landslide, thrashing Abbas's moderate Fatah party.
The government should "respect the democratic choice and results of the last legislative elections", Haniya reiterated before the meeting, declaring that the cabinet should work towards the "lifting of the blockade and end the suffering of our people".
Hamas and Fatah have been in deadlock for months over forming a unity government acceptable to the West, which froze direct aid since Hamas took power, flinging the Palestinian territories into unparalleled economic crisis.
The Islamists have steadfastly refused to bow to Western demands on recognising Israel, renouncing violence and abiding by past peace agreements.
British Prime Minister Tony Blair said on Monday that London was "prepared to talk to a national unity government", even if Hamas was part of it, provided the cabinet accepted those international conditions.
"You can't negotiate a two-state solution, Israel and Palestine, if one part of the people you're negotiating with is saying 'We don't want Israel to exist,'" Blair told his monthly news conference.
Abbas's arrival in Gaza came one day after a Palestinian cabinet minister said Hamas had reached agreement with Fatah on a broad coalition cabinet acceptable to Western donors.
"We've reached an agreement on everything, on the forming of the government, the name of the future prime minister, the criteria for appointing new ministers and the programme," said minister for prisoner affairs Wasfi Kabha.
Barghuti also said that both sides had agreed "to form a national unity government with independent and capable members".
But Hamas spokesman Fawzi Barhum denied any final agreement had been reached, saying only that "important progress" had been made.

Copyright AFP (Agence France-Presse), 2006