The groups declared a truce in December to end weeks of deadly violence, which intensified after Palestinian Authority Chairman Mahmoud Abbas, head of Fatah, called for new elections. The militant group Hamas won a parliamentary ballot in January.
In a separate incident, Palestinian militants kidnapped a Peruvian photographer working for the French press agency in the Gaza Strip on Monday, Agence France-Presse and Palestinian security sources said.
There was no immediate claim of responsibility for the abduction of Jaime Razuri.
Militants in Gaza have often abducted foreigners in the past, usually to try to put pressure on the Palestinian government to give them jobs.
Security officials said the kidnapping happened outside the AFP office in Gaza City, an area where many foreign news agencies have offices. They said the victim was standing at an intersection when about five masked men approached him, pushed him in a car and sped away.
The Tel Aviv-based Foreign Press Association, representing foreign journalists in Israel and the Palestinian areas, condemned the kidnapping of Razuri. "We utterly condemn the continued harassment of journalists in this way. We must be allowed to work freely and without fear of kidnapping in Gaza," the FPA said in a statement.
In two separate incidents in October, gunmen in Gaza seized and held a Spanish aid worker and a photographer working for the Associated Press news agency for several hours. In August, Gaza militants kept two journalists from the U.S. Fox News channel captive for two weeks.
Meanwhile, two media watchdogs said Monday that journalists suffered one of their deadliest years ever in 2006.
Paris-based Reporters without Borders (RSF) said at least 81 reporters and 32 media staff were killed in 2006 as a result of their jobs, saying the death toll was the highest since 1994 when scores of reporters died in the Rwandan genocide.