Khaled Abu Hilal, interior ministry spokesman, said that information from "third parties" confirmed that Fox News correspondent Steve Centanni, a 60-year-old American, and New Zealand-born cameraman Olaf Wiig, 36, were in good health.
The previously unknown Holy Jihad Brigades claimed responsibility on Wednesday for the August 14 kidnapping and warned the United States to free Muslim prisoners or the captives would face unspecified consequences. The three-day deadline passed at midday (0900 GMT).
Abu Hilal was speaking just before the deadline expired. He later said he hoped the journalists would be freed soon, denying reports quoting him as saying it might be about to happen.
Cabinet spokesman Ghazi Hamad said he hoped the crisis would soon be resolved.
"As we have heard from the minister of interior, things are positive and there is progress. We hope the crisis will be over in a few days," Hamad said.
"As we have heard from the minister of interior, things are positive and there is progress. We hope the crisis will be over in a few days"
Ghazi Hamad, Palestine cabinet spokesman
Meanwhile, the United States has said it will not make "concessions to terrorists".
Centanni and Wiig were seized as they were working on a story in Gaza City.
The kidnapping is the longest-lasting abduction of foreigners in the Palestinian coastal strip in more than a year.
The Hamas-led government has called for the men to be freed. Saeed Seyam, the Palestine interior minister, had suggested on Friday that the government had made indirect contact with the kidnappers through unidentified "Palestinian parties".
A videotape released on Wednesday showed the two men, dressed in tracksuits, sitting on a blanket in front of a black background. They appeared fairly relaxed and in good health. Both said that they were fine and being treated well.
Several prominent militant groups in Gaza have denied involvement and said the men should be freed.
Previous kidnappings of foreigners have usually ended after a few hours, or at most a few days, of captivity.