The ruling Fretilin party, which met in emergency session on Sunday, said Alkatiri had accepted the unanimous appeal of its committee not to resign.
The decision prompted the resignation of Jose Ramos-Horta, the country’s defence and foreign affairs minister.
"I decided to resign from the government until a new government is established," Ramos-Horta said through his spokesman. "I am ready to serve this nation in whatever position."
Ramos-Horta won a Nobel peace prize in 1996 for his nonviolent resistance to Indonesian rule.
Ovideo Amaral, the transport minister, also handed in his resignation, Portuguese news agency Lusa reported.
Fretilin have said they will now seek to "hold a dialogue with the president." Fransisco "Lu'olo" Guterres, chairman of the party, said they would seek the help of the Catholic Church to solve the crisis and called for a "meeting with political parties and non-governmental organisations to seek a final solution."
Guterres said Fretilin, "also asked that investigations be conducted into the illegal distribution of weapons and verify all allegations and accusations of the involvement of members and militants from Fretilin."
Gusmao demanded last week that Alkatiri step down after seeing an Australian documentary which alleged to have evidence that he had assented to have a hit squad armed and tasked with killing his rivals.
President Xanamo Gusmao called
on the prime minister to resign
Rogerio Lobato, the former interior minister, has been charged with distributing the weapons. But East Timor's independent prosecutor-general, who is conducting a UN-backed investigation, has said he does not have any evidence implicating Alkatiri.
The prime minister has repeatedly denied the allegations and refused to step down.
Calls for Guterre's resignation began mounting after violence in the capital, Dili, in late May which led to 21 deaths and more than 2,200 foreign peacekeepers being brought in. The unrest began after Alkatiri sacked some 600 deserting soldiers in March.