The truce was to take effect at 11 p.m., he told reporters.
"There will be a comprehensive cease-fire in Gaza to end all military demonstrations, all shooting will stop and random deployments (of armed men) will end," he said.
Earlier Tuesday, Prime Minister Ismail Haniyeh called for an end to Palestinian infighting and urged warring factions to unite in the struggle against Israel.
"This nation, this people will be united in front of the occupation and aggression and will not be engaged, despite the wounds of the past few days, in internal fighting," Haniyeh said in a televised speech.
In a rambling speech that stretched more than 40 minutes, Haniyeh also reiterated a call for a long-term truce with Israel and formation of a temporary Palestinian state alongside the Jewish state.
He said the truce could last as long as 20 years, after an independent Palestinian state is established in territories captured by Israel in the 1967 Mideast war.
Israel rejects a full withdrawal to the pre-1967 borders.
Hamas officials have proposed a long-term truce in the past.
Israel and the international community insist that the militant group fully recognize Israel's right to exist. Hamas, which is committed to Israel's destruction, has repeatedly rejected that demand.
Israeli Prime Minister Ehud Olmert made a surprise visit to Jordan on Tuesday for talks with King Abdullah II on ways to revive Mideast peacemaking.
Olmert's visit came in response to an invitation by Abdullah, who is eager to see Israel resume peace negotiations with the Palestinians, a senior palace official said.
CBS News correspondent Robert Berger reports that Olmert's office says the two men discussed developments in the Gaza Strip, where fighting among rival Palestinian factions has raised fears of civil war.
The palace also said Abdullah intends to invite the warring Palestinian Hamas and Fatah factions to talks in Jordan to mend their differences.
Fierce gun battles erupted in the streets of Gaza City early Tuesday between Hamas and Fatah forces, leaving at least three people dead and shattering hopes that a shaky truce agreed to Sunday might survive.
The sound of automatic gunfire could be heard throughout Gaza City, and a Fatah security installation was attacked with mortar fire.
Masked Hamas gunmen set up makeshift checkpoints on main roads, forces from the two sides took up strategic positions, and terrified residents remained indoors in anticipation of further fighting.
Berger says fighting erupted at a hospital and at a key security agency controlled by moderate Palestinian President and Fatah leader Mahmoud Abbas.
At least 18 people were wounded, including five schoolchildren caught in the crossfire of a gunfight, hospital officials said. A Hamas gunman was kidnapped and a top Fatah official's car was attacked by gunfire — the latest unrest in a week of factional fighting that shows few signs of easing despite Sunday's truce declaration.
"It's a real war. Since the morning, I've been praying to God that this is going to end," said Suleiman Tuman, a 53-year-old shopkeeper who was trapped in his Gaza City grocery store by the fighting.
"Both sides used to fight the Israelis together. Now they are directing their weapons toward each other, and we're in the middle," he said. "Both sides are responsible for this war."
Dozens of masked Hamas gunmen, armed with grenades and Kalashnikov rifles, patrolled the streets outside his shop.
Hamas and Fatah have been locked in a power struggle since the Islamic group defeated Fatah in legislative elections in January. Abbas' Fatah party, which seeks peace with Israel, controls the presidency, while the radical Hamas, which is committed to Israel's destruction, controls parliament and the Palestinian Cabinet.
The latest wave of fighting broke out last week, with tensions heightening after Abbas announced plans to call early elections over the weekend. Hamas has condemned the plan as a coup.
The heavy fighting began early Tuesday after a member of the Fatah-controlled intelligence service arrived at Gaza City's Shifa hospital with a broken leg. He was accompanied by two armed colleagues. Hamas militiamen guarding the hospital blocked the entry of the armed men and attempted to arrest them.
When more Fatah forces arrived, they were fired upon, sparking the gunfight, Fatah officials said.
Hamas accused Fatah of storming the hospital, and said a 23-year-old member of a Hamas police unit was killed. It also said one of its men was kidnapped.
Hamas and Fatah officials said they remained committed to the truce, and accused each other of violating the deal.
The tensions turned violent last week after three young sons of a Fatah security officer were gunned down. The fighting worsened after Abbas' announcement Saturday that he would call new elections to end the impasse.