Ismail Haniyeh, the prime minister of the Hamas-led government, met with the news organization's Jerusalem bureau chief, Eli Fastman, and its chief correspondent in Israel, Jennifer Griffin. President Mahmoud Abbas also scheduled a meeting with them.
U.S. officials said they were in touch with Abbas' office, Palestinian security officials and the Israelis to see if they can help secure the journalists' release.
"Certainly we are concerned about their safety, that is why we are working to ensure their freedom," said Micaela Schweitzer-Bluhm, a spokeswoman for the U.S. consulate in Jerusalem.
She said it was still unclear who was holding the journalists.
Steve Centanni, 60, a U.S. citizen, and Olaf Wiig, 36, of New Zealand, were seized by masked gunmen near the headquarters of the Palestinian security services.
"The family's holding up OK," Centanni's brother, Ken, said Tuesday from his San Jose, California, home. "We're confident things will resolve themselves. But we haven't heard from the kidnappers yet."
No one has claimed responsibility for Monday's kidnapping, and police said no one has come forward with demands. In previous kidnappings of foreign journalists, militants have quickly contacted authorities demanding government jobs, money or the release of jailed relatives. The journalists were usually freed a few hours after being seized.
Major militant groups denied they had anything to do with the new abduction.
On Tuesday, Fastman and Griffin met in Gaza with Haniyeh, who reassured them that the Palestinian security forces would use all its power to " put an end to it soon," said Ghazi Hamad, a government spokesman.
Prime Minister Helen Clark of New Zealand dispatched diplomats to Gaza to assist in any contacts for their release. She said in Wellington she was "very concerned" about the kidnapping.
Wiig's wife, Anita McNaught, said Fox representatives told her negotiations for their release were already under way. But officials in Gaza said no contact had been established with the kidnappers.
Ken Centanni said that while the situation was scary, his large family is trying to remain hopeful. The family was always worried something like this would happen, but his brother seemed to have little fear.
"That's his life — he's married to his career, and he's a very good reporter," Ken Centanni said, adding his brother had reported all over the Middle East. "He loves the human interest side. I can't help but think that he has compassion for the kidnappers. That's the kind of person my brother is."
Interior Ministry spokesman Khaled Abu Hilal called on Palestinians to give the authorities any information they had regarding the missing journalists and denied that the kidnappers had any connection with al Qaida.
He emphasized that Hamas opposed any attacks on journalists, regardless of their nationalities.
"We hope the kidnappers feel this and deal with the issue this way, so their release will be faster," he said.
Nabil Abu Rdeinah, an Abbas aide, said the president ordered all security forces to work on tracking the two journalists. "This is an unacceptable act. We condemn this operation and hope we would succeed to find a peaceful solution very soon," he said.
An investigator in the case, speaking on condition of anonymity, said suspicions were focusing on a renegade group from an established Palestinian militant organization, but he declined to give further details. The car in which the journalists were taken has been identified, he said.
Centanni was behind the wheel of the Fox vehicle, marked in large letters "TV," when the gunmen pulled up and stopped them, a Fox employee said. A Palestinian who was with them was forced onto the floor at gunpoint, and the two journalists were taken away.
An official following the investigation said the getaway car was spotted driving south along the coastal road.
Police and security forces were deployed at major intersections and roads in Gaza immediately after the kidnapping.
Several foreigners have been kidnapped in Gaza by small groups seeking the release of relatives from jail, jobs or other personal favors. All have been freed within hours or a few days without harm.