With the previous 48-hour deadline expiring on Monday, Aljazeera reported that the self-styled Islamic Army in Iraq (IAI) would delay the deadline by another day.
The IAI called on Paris to rescind a ban on religious symbols - in particular Muslim headscarves - at schools and universities.
The newsmen, Radio France correspondent Christian Chesnot and Georges Malbrunot of Le Figaro newspaper, were also shown in a video.
Both men called on the French government to revoke the headscarves ban and on the French people to demonstrate against the legislation.
France has been engaging in 11th hour diplomacy, dispatching two envoys to the Middle East to try and secure the release of the two journalists.
Radio France's Christian Chesnot
is very experienced in the region
In an interview with Aljazeera, French Foreign Minister Michel Barnier made an impassioned plea to try to save the two journalists' lives as an ultimatum issued by their kidnappers neared expiry.
He said: "These two men of goodwill have always shown their understanding for people and their fondness for the Arab and Muslim world.
"I call for their release in the name of principles of humanity and respect for the human being which are at the very heart of the message of Islam and the religious practices of Muslims."
"Islam is a religion that defends peace and tolerance and respect for human life.
"Islam has become the second religion in France. The five million Muslims in France perform their full religious tenets in complete freedom."
The main Sunni Muslim religious organisation in Iraq also renewed its appeal for the pair's release.
"In the name of the Association of Muslim Scholars we urge the kidnappers to release the two journalists," said Shaikh Abd Al-Sattar, a member of the committee, speaking to Aljazeera on Sunday.
He simultaneously appealed to France to reconsider its decision to ban prominent religious insignia, including Muslim headscarves, in French state schools.
Earlier at a press conference in Cairo, Barnier said the two journalists were doing their job in Iraq to explain to the world the reality of the situation of the Iraqi people.
Le Figaro's Georges Malbrunot was
seized with Chesnot near Najaf
He also said a top diplomat had been dispatched from Paris to Baghdad to press for the release of the two men.
But his government has vowed not to bow to the demands of the kidnappers which want the repeal of a controversial French law banning the Islamic headscarf in state schools.
Chesnot and Malbrunot disappeared in Iraq on 20 August, the day they were due to have left Baghdad for Najaf.
On Saturday Aljazeera television broadcast images of the two men - both Middle East experts with years of experience in the region - along with the ultimatum from the IAI.
The kidnappers issued a 48-hour ultimatum to France over the headscarf ban, but did not specify what would happen after the deadline expires.
Approved earlier this year and set to go into effect on Thursday when classes resume, the French law bans the wearing of all "conspicuous" religious insignia in public schools, including large Christian crosses, Jewish skullcaps and Sikh turbans.
Although all religious signs are covered by the prohibition, French Muslims believe they are the main target of the law and there has been an angry reaction among many in the community of five million - the largest in Europe.
In France, Muslim leaders condemned the hostage-taking. Fuad Alaui, secretary general of the Union of Islamic Organisations of France, described the kidnappers' demands as "hideous blackmail".
Alaui said the law banning conspicuous signs of faith in state schools applied to all French citizens.
In an interview with Aljazeera, Dr Fathi Yakun, founder of the Islamic Movement of Lebanon, denounced the kidnapping of journalists in Iraq.
"The French stance in opposing the war against Iraq and its continuous support to the Arab and Islamic questions along with France's opposition to take part in any military action against Iraq, was quite enough to justify freeing these hostages," he said.
"We call upon them in the name of Islam and the higher Islamic interests to immediately free the French hostages," he continued.
He also criticised the kidnappers' demands that France renege on its ban on Muslim headscarves, saying "we don't see any [Islamic] interests in linking the headscarves question to the US war against Iraq".
In an interview published in an Italian newspaper on Monday, Iraqi interim Prime Minister Iyad Allawi said: "No civilised country can draw back. The campaign against terrorism must be a global one. Because the challenge really is global.
"Neutrality doesn't exist, as the kidnapping of the French journalists has shown," he told the Corriere della Sera newspaper.
"The French are deluding themselves if they think they can remain outside of this. Today, the extremists are targeting them too," Allawi said.