Israeli media reports suggested that the four ministers - Silvan Shalom, the foreign minister, Limor Livnat, responsible for education, Yisrael Katz, the agriculture minister and the health minister, Danny Naveh - were to defy Netanyahu.
Netanyahu was elected as Likud leader last month after Ariel Sharon, who helped found the party, split it by leaving to form his own centrist party, Kadima. He had been frustrated by criticism from the right of the party over his withdrawal from Gaza.
The walkout had been planned for earlier in the week but was postponed out of respect for the prime minister who suffered a stroke last week and is now in a critical condition in hospital.
Netanyahu ordered the ministers to tender their resignations from the government on Thursday morning, shortly before voting begins to determine the list of Likud candidates to run in national elections on 28 March. Reports on Israeli radio on Thursday said that the ministers refused to comply and instead said that they would resign only on Sunday.
One unnamed minister was quoted by the YNETnews website as saying: "We won't obey [Netanyahu's] orders to resign."
The order was issued by Netanyahu on the eve of Likud's primary elections. The aim was to pressure ministers to follow through on his instructions or risk not winning a place on the party ticket.
Ynet quoted a source close to the ministers as saying: "Netanyahu put a gun to our heads on the eve of the Likud primaries. The four cabinet ministers have decided that at this point they will not agree to his request."
Sharon's likely successor as head of Kadima, the interim prime minister, Ehud Olmert, received a pre-election boost when newspaper opinion polls predicted that the party would crush its rivals, even without Sharon.
The polls suggest that Likud's current tally of 40 seats might drop to as few as 13 in the 120-member Knesset.
The hawkish Netanyahu, a former prime minister, had hoped to increase Likud's chances by positioning himself as an experienced leader with a united party behind him. But in-fighting within the right-wing group might hamper these efforts.
If the four Likud ministers resigned, Olmert would be able to appoint new ministers in his caretaker government until the elections.