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GAZA CITY, Gaza (CNN) -- Two Fox journalists kidnapped by militants two weeks ago in Gaza and freed appeared to be in good health as they embraced family and co-workers in an emotional reunion.

Fox reporter Steve Centanni and photographer Olaf Wiig were released shortly after noon Sunday and dropped off at the Beach Hotel in Gaza City, where they were greeted by a swarm of people offering hugs. The hotel is a popular place for journalists.

The two men later crossed into Israel and left for Jerusalem. The Palestinian government had condemned the kidnapping and the men's families pleaded publicly for their release. (Watch as freed journalists prepare to cross into Israel -- 1:52)

Hours before their release, a video on the Palestinian news service Ramattan TV showed the two reading statements proclaiming they had converted to Islam. But the two later explained they had done so at gunpoint, and that the conversion was not real.

Centanni spoke to Fox News Network immediately after his release.

"I'm a little emotional because this is overwhelming, but I'm really fine, healthy, in good shape," he said.

"Somebody did the right thing somewhere because here I am, and I must first off thank everybody for their support and for all the work that this team here has done," he said. "My family and friends, I understand, have been very helpful." (Watch Centanni and Wiig's first moments of freedom -- :59)

Centanni and Wiig were snatched off the streets on August 14 by masked gunmen and held by a previously unknown group calling itself the Holy Jihad Brigades.

"We were driving down a narrow side street in Gaza City and there was a car stopped in front of us," Centanni said. "Before we realized what kind of car had stopped, four masked gunmen came over."

Centanni said he and Wiig were shoved into a small Toyota and their captors draped black hoods over their heads before speeding away.

"That was the beginning of our torment that night," he said.

A spokesman for the Palestinian Ministry of Interior, Khaled Abu Hilal, said the journalists' release "is the payoff of the continuous efforts from different Palestinian sides to secure their safety and release."

Hilal did not provide details on the process of their release but did confirm the Palestinian Authority will secure their exit from Gaza.

Palestinian Interior Minister Saed Sayyam said at a news conference, "There is a promise that similar actions would not be happening again," although he did not say who made that promise.

"Regarding the issue of specifying the identity of the kidnappers, that is to be investigated by the Palestinian government," he said. "Our main concern at the beginning was to secure their release and not to put obstacles in front of those who were involved to solve this case."

He added, "Whoever was the side responsible and whatever political backgrounds were standing behind it -- this is absolutely rejected. It is the responsibility of the security forces to investigate."

The journalists thanked British and U.S. officials and praised Palestinian officials for helping secure their release. (Watch freed journalists speak after release -- 4:24)

"I just hope this never scares a single journalist away from coming to Gaza to cover this story because the Palestinian people are very beautiful, kind-hearted loving people who the world needs to know more about," said Centanni at a brief news conference.

Wiig echoed those remarks. "That would be a great tragedy for the people of Palestine and especially for the people of Gaza. Your story doesn't get very well told because it is difficult to work here and anything that -- any little discouragement -- an incident like this could give a network an excuse not to be here and that would be a great tragedy for the people of Gaza," he said.

In Kennebunkport, Maine, President Bush was informed by senior staff about the developments.

"The president is pleased the journalists were released and will soon be reunited with their entire families and colleagues," said White House Deputy Press Secretary Dana Perino.

The initial condition for release was that all Muslim prisoners "in the jails of America" be released.

The United States refused to offer concessions to their demands, keeping with its long-standing policy.

Pressure had mounted from Palestinians for the kidnappers to release the journalists.

A Palestinian prisoners' rights group said that even Palestinian prisoners being held in Israeli jails asked the kidnappers to release the journalists immediately and unconditionally.