Story Highlights• NEW: Cease-fire begins 3 a.m. Tuesday (7 p.m. Monday ET)
• NEW: Agreement: Armed militants off street, except police
• Factions' leaders will exchange kidnapped prisoners
• At least 50 kidnapped since fighting broke out last Thursday
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GAZA CITY (CNN) -- Rival Palestinian factions Hamas and Fatah agreed to a cease-fire late Monday in a bid to end four days of violence that killed at least 29 people in Gaza and the West Bank.
The cease-fire, announced by Palestinian Foreign Minister Mahmoud Zahar, began 3 a.m. Tuesday (7 p.m. Monday ET).
In the hours before the deadline, gunfire and explosions could still be heard in Gaza City.
The agreement calls for both sides to withdraw their armed militants from the street, except for Palestinian police, and stop all clashes, as well as refrain from making inflammatory comments.
Since fighting erupted late last week, Fatah and Hamas militants have kidnapped more than 50 members of each other's groups, most of them in the West Bank town of Nablus, Palestinian security sources said.
Hamas and Fatah leaders have agreed to exchange kidnapped prisoners and participate in a face-to-face meeting, Zahar told reporters.
Hamas has controlled the Palestinian parliament since last year, when elections ended decades of Fatah control.
However, the Palestinian Authority presidency is held by Fatah leader Mahmoud Abbas.
Talks aimed at forming a power-sharing government were suspended after the latest outbreak of violence, which began Thursday when a Hamas operative was killed by a bomb in the Jabalya refugee camp in Gaza.
Sunday, West Bank Hamas leader Fayyad al-Arba was at a bank in Nablus when gunmen with the Al Aqsa Martyrs Brigades -- the armed wing of Fatah -- walked up a flight of stairs to the entrance, pointed their guns at him, and forced him out.
The Associated Press released video of the abduction, as well as a separate clip of a man identified as Abu Jabal, head of Al Aqsa Brigades in Nablus, saying, "Our demand is the resignation of the interior minister and the suppression of the executive force in Gaza."
A recurring sticking point in negotiations between the two groups is Hamas' refusal to recognize Israel's right to exist. Western nations have frozen funds for the Palestinian territories until this prerequisite is met. Another bone of contention is how the competing security forces should divide responsibilities.
Palestinian legislator Saeb Erekat said Abbas has declared that if an agreement on a unity government is not reached within three weeks, then Abbas will issue a presidential decree ordering early elections.
Hamas said it will boycott an early vote.
Palestinian Hamas security members stop a car at a checkpoint in Gaza City on Monday.