Story Highlights• NEW: Fatah and Hamas ordered to withdraw from the streets
• Palestinian Interior Minister al-Qawasmi resigns as Hamas-Fatah truce collapses
• Cease-fire began early Monday; ends as gunbattle erupts in Gaza City
• 2 gunmen dead, 10 wounded in fighting; follows deaths of 4 militants Sunday
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(CNN) -- A cease-fire between Hamas and Fatah has been restored, a Palestinian government spokesman said Monday.
"We have an agreement, and we have confidence that this agreement should be implemented this night," Ghazi Hamad told reporters in Gaza City.
Palestinian Authority President Mahmoud Abbas and Palestinian Prime Minister Ismail Haniya have issued orders to security forces from Fatah and Hamas respectively to withdraw from the streets, Hamad said.
"Hamas and Fatah -- both of them -- give orders to their elements in the street to withdraw and to stop all military conflicts and clashes in the streets and to return all kidnapped people and to stop the media inciting," he said.
The announcement about the cease-fire came hours after an Egyptian-brokered truce ended early Monday, when shooting resumed between rival militias.
The gunbattle left two gunmen dead and 10 others wounded, Palestinian security sources said.
Violence between the factions left four dead on Sunday.
Interior Minister resigns
According to the sources, the gunbattle broke out near the Fatah intelligence headquarters in northern Gaza City. The dead were the bodyguards of a local Fatah leader.
In protest of the ongoing violence in Gaza, Palestinian Interior Minister Hani al-Qawasmi resigned Monday, one of his assistants told CNN.
According to the assistant, Haniya accepted al-Qawasmi's resignation.
His resignation was a blow to the Palestinian unity government, formed earlier this year in an effort to end the deadly factional fighting concentrated in Gaza.
One of the major sticking points in forming the Fatah-Hamas government has been the portfolio of the interior minister and choosing who would fill the key position.
The interior minister has control of Palestinian security forces.
Amid frustrations over the inability to enact a Gaza security plan, al-Qawasmi had tendered his resignation to Haniya a few weeks ago, but the prime minister did not accept it.
Hamas and Fatah officials had told reporters shortly after midnight Monday that they would begin observing a cease-fire at 1 a.m. (6 p.m. Sunday ET), but the truce never made it to daybreak.
Under the agreement, all checkpoints were required to be dismantled, gunmen from both sides were required to be withdrawn from the streets and any hostages held by either side were to be released.
Hamas won the Palestinian elections last year, ending decades of rule by the Fatah party. Hamas took control of the parliament and the prime minister post, although Fatah's Abbas maintained the title of president.
After months of deadly clashes, the two sides met recently to build a new government aimed at ending the fighting.
Hamas has been labeled by the U.S. State Department as a terrorist organization. The group's military wing, Izzedine al Qassam, has admitted responsibility for terrorist attacks against Israel.
CNN's Kevin Flower, Shira Medding and Waffa Munayyer contributed to this story.