Top Hamas leaders Mahmud Zahar and Haniya made the announcement at a news conference in Gaza City following talks with the moderate Palestinian Authority president, two days after a Hamas-led parliament was sworn in.
Mr Abbas will hand over the official nomination letter at 6pm on Tuesday during a meeting with Mr Haniya, Mr Zahar told journalists.
The Gaza leader of Hamas, which is branded a terrorist organisation by the European Union and United States, said he expects the group to finalise a coalition line-up within an initial three-week period allotted to the new prime minister.
"I think we can declare the cabinet during the three weeks," Mr Zahar said.
Coalition talks
Faced with stinging Israeli sanctions and the prospect of cuts in aid from Washington and the EU, not to mention the faction's lack of government experience, Hamas is keen to form a national coalition.
To that end, talks with other parliamentary factions would continue in order to agree on the make-up of the new cabinet, Mr Zahar and Mr Haniya said.
Hamas representatives on Monday started to thrash out the line-up of the new-look government with the Popular Front for the Liberation of Palestine (PFLP) and the Democratic Front for the Liberation of Palestine.
PFLP politburo member Rabah Muhanna said the faction had agreed in principle to join the incoming administration.
Mr Haniya confirmed that Hamas would also talk to Abbas's Fatah party, although several senior party lights have ruled out joining the government that Mr Abbas has said already faces a "serious financial crisis".
Talks on forming a government would be held with "Fatah and other personalities and political forces ... inside and outside" the Palestinian territories, he said.
Payments suspended
Israel's cabinet voted on Sunday to suspend immediately payment of customs duties and VAT to the Palestinian Authority, estimated at US$50 million a month.
Washington also wants $50m in aid returned by the Palestinians, in light of Hamas's control of the government.
But the United Nation's Middle East envoy, Alvaro de Soto, said on Monday that Israel has no right to freeze the transfers and should have at least waited for the new government's formation.
Mr De Soto, who met Israeli defence officials after the cabinet imposed a series of financial and travel sanctions, said the freeze was "problematic for several reasons", especially as the money belonged to the Palestinians.
In the wake of the sanctions, the EU, the biggest Palestinian donor, and Russia stressed they would continue to provide as much financial support as possible.
"We will continue to support the Palestinian Authority until the new government is formed and on that we are trying to find the necessary resources," EU foreign policy chief Javier Solana told reporters.
Russian Foreign Minister Sergei Lavrov also said that Moscow would continue to send "urgent aid".
Although Western powers are reluctant to channel money directly into what they consider a terrorist organisation, they have also cited concern that a drastic drying up in funds will merely push Hamas closer to backers in Iran.
Iran support
Iran's supreme leader Ayatollah Ali Khamenei called on Muslims worldwide on Monday to provide a "yearly financial aid package" to the Palestinians during talks in Tehran with Hamas's visiting political leader Khaled Meshaal.
US Secretary of State Condoleezza Rice will on Tuesday start a Middle East visit, during which she is likely to press home demands that Hamas renounce violence, recognise Israel's right to exist and abide by previous Palestinian agreements.
Hamas, which refuses to recognise the Jewish state's right to exist and has carried out dozens of suicide attacks in the past five years, has so far dodged calls by Mr Abbas to recognise past agreements signed with Israel.
Aziz Duweik, the new Hamas speaker of parliament, ordered a freeze on all decisions made by outgoing MPs at a meeting last week, which included approval for Mr Abbas to appoint members of a new constitutional court.