Nabil Abu Rudina, the president's spokesman, said the government was "coming along" and there was "no serious problem in the consultations".
"We have needed some days to discuss all the problems. We will continue our discussions tomorrow and a national unity government will be formed in less than a week," he said.
Talks to continue
The three-hour meeting on Sunday followed last month's agreement in Mecca signed by Abbas, representing the Fatah movement and Ismail Haniya, the prime minister-designate, on behalf of Hamas.
Officials hoped to meet a constitutional deadline of March 21, the end of a five-week period allotted for negotiations.
Abbas and Haniya are expected to continue talks on Monday and Tuesday.
One of three main unresolved issues after Sunday's meeting is who would be interior minister, a position which controls security services, Palestinian sources close to the talks said.
One source said Abbas did not endorse Hamas's candidate for the job, Hamouda Jerwan, a retired general.
The leaders also could not agree on who would be deputy prime minister and whether a Syrian-based Palestinian faction should be allowed to join the government, the sources said.
A final political platform has yet to be drafted, they added.
Under the power-sharing agreement, Hamas can nominate 12 cabinet ministers, including three independents, while Fatah can propose eight, including two independents.
Haniya will remain prime minister, while Fatah will be able to fill the post of deputy prime minister.
Last month, the leaders of Hamas and Fatah signed an agreement in Mecca, following a political crisis which degenerated into deadly clashes between the two groups in the Gaza Strip.
After democratic elections last year, the government formed by Hamas was paralysed by a punishing Western aid freeze and the withholding by Israel of Palestinian tax revenue.
Hamas is considered a "terrorist" organisation by Israel, the United States and the European Union.
The Quartet of main players in the Middle East peace process - the European Union, Russia, the United Nations and the United States - has called for any new Palestinian administration to renounce violence, recognise Israel and honour previous interim peace deals.