"There can be no progress with an administration in which there are terrorist organisations as members," said a statement from the office of Ehud Olmert.
In the occupied West Bank, meanwhile, a bomber blew himself up, and a second Palestinian militant was shot by Israeli troops as he fled during an arrest operation in the flashpoint town of Jenin, the Islamic Jihad group said.
There were no casualties among the soldiers targeted by the bomber, Israeli military sources said.
The latest violence came as Israeli politics resumed in earnest, after a brief lull induced by the illness of Prime Minister Ariel Sharon, with four Likud ministers set to quit the cabinet.
Security challenge
The flare-up also illustrated the security challenge facing Israel's acting Prime Minister as he faced a possible increase in unrest ahead of Palestinian parliamentary elections on January 25.
In his first phone conversation with US President George W Bush, on
Thursday, Mr Olmert said there could be no progress in the Middle East peace process if Hamas entered a Palestinian government.
He urged Palestinian leader Mahmud Abbas to "take steps against terrorism and disband the terrorist organisations," according to a statement from his office.
Israel and the US both regard Hamas, which is contesting parliamentary elections for the first time, as a terrorist organisation despite its entry into the democratic process.
Israel has banned Hamas, responsible for the majority of anti-Israeli attacks during the last five years of violence, from campaigning in east Jerusalem.
Mr Bush urged Hamas to change its policy towards Israel.
The US president also asked Mr Olmert to convey his esteem to Mr Sharon's sons, Omri and Gilad, adding that it was "very important" that the prime minister recover from his massive stroke.
Mr Sharon remains in intensive care, in "serious but stable" condition.
His doctors have expressed amazement at the 77-year-old leader's recovery, with upbeat reports fueling the resumption of electioneering for March parliamentary elections.
Doctors said a new scan carried out Thursday found no traces of blood in the prime minister's brain, making it possible to remove the tube that had been inserted into his skull to drain it away.
Chief neurosurgeon Felix Umansky said he believed Sharon was now "out of danger," but said earlier that infection was now the principal concern.
"Little by little, he is giving us more signs that he is getting better but he will not wake up for the next day or two," the Argentine doctor said.
Party primaries
In the political arena, the chairman of Mr Sharon's old right-wing party, Benjamin Netanyahu, has launched a vitriolic attack on the caretaker government, convincing the four remaining Likud ministers to resign.
Three of them have already submitted letters of resignation to avoid implementing Olmert's plans to allow Palestinians to vote in east Jerusalem this month.
Foreign Minister Silvan Shalom confirmed that he would follow suit Friday. Israeli media tipped Justice Minister Tzippi Livni, a close Sharon ally, to take over the portfolio until March 28 elections.
The Likud, which has been in crisis since Mr Sharon abandoned the party create his new centrist movement Kadima six weeks before his stroke, is at loggerheads with Mr Olmert, who was one of the first from Likud to defect to Kadima.
Likud primaries saw hardline opponents of last year's pullout from Gaza take more than half of the top positions on the party slate.
But there was a personal reverse for former cabinet minister Uzi Landau who quit the government in 2004 to spearhead the opposition and only made 14th place.
In a boost for Mr Sharon's new party, the staunchly secular Shinui, which was the third party in the outgoing parliament but has seen Kadima usurp the ideological centre ground, was left in disarray after its primaries.
Its leader, former justice minister Tommy Lapid, only just won re-election and his deputy Avraham Poraz was ousted, prompting reports of an imminent split.