A previously unknown group The Holy Jihad Brigades claimed responsibility for the kidnapping and released a video of the men who were taken captive in Gaza earlier this month.
"This is the first information we have had about the two men since they were kidnapped 10 days ago," Clark said in a statement.
"I am pleased that they appear to be well and that they say they are being treated reasonably. Nevertheless, I remain deeply concerned for their safety."
New Zealand officials in the region were continuing their "intense consultation" with Palestinian authorities and others in an attempt to win the freedom of the pair, Clark said.
Wiig's family said in a statement the video was good news.
"We are relieved to have it confirmed that Olaf and Steve are alive and well and we wait anxiously for their release," they said.
But the United States has rejected the kidnappers demands and insisted on the unconditional release of the two men.
Militants demands
In exchange for the men’s release, the Holy Jihad Brigades has demanded that all Muslim prisoners in the US be released within 72 hours.
"We will give you one chance that will not be repeated -- the liberation of Muslims detained in American prisons in exchange for the detainees in our hands," the group said in a statement.
"As we have maintained publicly, we do not make concessions to terrorists," a State Department spokesman said.
“We continue to call for the release of these journalists unconditionally,” he said.
The State Department spokesman replied that the US government "strongly condemns the kidnapping of these independent journalists, who were in Gaza to tell the Palestinian story to the world".
US Secretary of State Condoleezza Rice has spoken with Palestinian President Mahmoud Abbas about the journalists, officials said.
A spokesman thanked the Palestinian leader and his security services for their help in trying to obtain the journalists' release.
"But we ask that President Abbas and the security services continue to do all they can to find the two journalists and obtain their safe release," he said.
Video gives Fox some comfort
Fox News has also called for the men to be freed.
In New York, Fox senior vice president John Moody issued a brief statement.
"We trust that the abductors understand they are responsible for Steve and Olaf's welfare and safe return,” it said.
“We ask for their immediate release.”
But it seems the tape provided some relief too.
"We're encouraged that our colleagues appear to be alive and well in the tape that was released," he added.
AFP