The Palestinian security services and the interior ministry have been told to "take all necessary measures" to secure the release of the BBC's Alan Johnston.
Palestinians have held regular protests in support of Mr Johnston
The case of the abducted reporter was discussed at a special cabinet meeting.
Palestinian journalists and media workers staged fresh protests in the West Bank and Gaza on Saturday to press for his release.
He was last seen in Gaza on 12 March and is believed kidnapped. There have been no claims of responsibility.
If abducted, Mr Johnston - the only international reporter based in Gaza - will have been held captive longer than any other journalist there.
Saturday's rallies - in Ramallah, Nablus, Jenin and Gaza City - were the latest in almost daily protests calling for Mr Johnston's release and urging the Palestinian authorities to do more to find him.
On Friday, children paraded in Gaza in support of Mr Johnson, who was also remembered at prayer meetings.
The BBC's Mike Sergeant in Jerusalem says that there is mounting frustration and anger in Gaza and the West Bank.
Many Palestinians feel Mr Johnston's abduction has made their story much harder to tell, our correspondent says.
On Thursday a British diplomat had talks about Mr Johnston with Palestinian Prime Minister Ismail Haniya, a member of the militant Hamas movement.
It was the first meeting with Mr Haniya for the UK government, which normally boycotts Hamas as a terrorist group.
The BBC has received thousands of messages of the support from users of the News website demanding the release of Alan Johnston.
It describes Mr Johnston as a highly experienced and respected reporter.
He joined the BBC World Service in 1991 and has spent eight of the last 16 years as a correspondent, including periods in Uzbekistan and Afghanistan.