In a statement, Mohammed Morsi said there was "no room for dialogue with the criminals".
He was speaking after a video emerged apparently showing the three police officers and four soldiers pleading for their release.

The kidnappers are said to be demanding the release of political detainees.

Mr Morsi's statement came after a meeting with senior politicians on Sunday.

The president wrote on his Twitter feed that "all options are on the table" to free the hostages and that the government in Cairo would "not succumb to blackmail".

The seven men were captured while travelling in minibuses in northern Sinai, east of the city of El Arish.

In the unverified video posted online on Sunday, seven blind-folded men are seen with their hands on their heads. One appeals to President Morsi to rescue them, by securing their freedom through the release of political detainees from Sinai.

The abductions have prompted angry police to shut down border crossings with Gaza and the occupied territories until the hostages are released.