"We want to share the pain of those who are ready to share it with us," Turkish Foreign Minister Ahmet Davutoglu was quoted as saying by Anatolia news agency in an interview with state-run television TRT Haber late Tuesday.
Armenians say up to 1.5 million of their forebears were killed in a 1915-16 genocide by Turkey's former Ottoman Empire. Turkey says 500,000 died and ascribes the toll to fighting and starvation during World War I. "It is necessary to keep channels open in order to share history," said Davutoglu.
Turkey and Armenia have no diplomatic relations as Ankara closed its border with Yerevan in 1993 because of its war with Azerbaijan over the disputed region of Nagorny Karabakh.
In 2009, Turkish and Armenian foreign ministers signed protocols to establish diplomatic ties and reopen their shared border. The protocols also called for a joint commission to examine the two countries' shared history.
But the normalisation process has stalled after Turkey faced backlash from its traditional ally Azerbaijan and the opposition at home. Ankara has also complained that genocide resolutions introduced at third countries' parliaments are hampering the process.
The French Senate passed a law last year outlawing the denial of the Armenian genocide, which drew fury from Turkey accusing President Nicolas Sarkozy of pandering to an estimated 400,000 voters of Armenian origin ahead of an April-May presidential election.
France had already recognised the killings as a genocide, but the new law sought to go further by punishing anyone who denies this with up to a year in jail and a fine of 45,000 euros ($57,000).
On Tuesday, the French Constitutional Council labelled the law "unconstitutional," which was quickly welcomed by Turkey. But Sarkozy ordered his government to draft a new law. Davutoglu accused Sarkozy of "waging a war against French culture and law."
"At first, he waged war against history and freedom of expression and now he is waging war on the French Constitutional Council," he added.