The statement posted on an internet site is claiming to be from the "higher command" of the Islamic Army in Iraq. The statement said: "We warn you not to bombard us as you did on the day when we intended to deliver the hostages to you."
Christian Chesnot, 37, of Radio France International, and Georges Malbrunot, 41, who works for Le Figaro, were captured on route to Najaf soon after August 20 and were expected to be released last week.
The message on the website and the new demand is the first confirmation for over a week that the pair are still alive.
French Prime Minister Jean-Pierre Raffarin said: "We always take this type of information seriously... We are trying to check its authenticity at this time."
He told RTL radio the situation was "worrying" but added: "Nothing is calling into question the confidence we have in a favourable outcome."
As well as setting the ransom, the kidnappers called for a truce with Al Qaeda leader Osama Bin Laden and demanded a promise of no military and commercial dealings with Iraq. The demands appeared to be directed at France, which has been surprised by the hostage takings because it has played no military part in the war in Iraq or Afghanistan.
Ten days ago, the kidnappers released their first set of demands, telling France it was to withdraw a law banning Muslim girls from wearing headscarves at school. Paris refused and the law went into force last Thursday.
The French authorities are treading carefully and face the dilemma of whether to pay the ransom, after the previous efforts to resolve the situation with Iraqi militants failed.
France is known to have previously paid hostage takers to get its people home safely.
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