Abu Rudina said: "President Abbas is carrying a list of Fatah's candidates and expecting that Hamas would present its list ... and the other factions to give their final response."
Hamas on Saturday submitted its list of nominees for ministerial posts in the government to the prime minister designate.
Salah Bardawil, a Hamas spokesman, said that of the 12 cabinet ministers proposed by Hamas, seven are from the West Bank and five from Gaza.
"The Palestinian people are in desperate need of leaders to solve their daily problems and security"
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None of the Gaza candidates served previously in parliament or the government, he said.
Abbas and Haniya was originally due to meet on Saturday but it was put back to Sunday.
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.
Salam Fayyad, a former finance minister, is expected to return to the post and is also a leading candidate for 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.