French investigators believe they are close to identifying the second man who killed a priest in his own church on Tuesday, French media report.
They believe he could be the same person as a man they have been hunting since last week after a tip-off.
One of the two church attackers has already been named by police as 19-year-old Adel Kermiche.
So-called Islamic State has released a video of what it says are the two men pledging allegiance to the group.
Fr Jacques Hamel, 86, had his throat cut in the attack at a church in a Normandy suburb, while a worshipper was left seriously injured.
Both of the attackers were shot dead by police after they took hostages.
Officers are said to have found an ID card at the home of Kermiche belonging to an individual named as Abdelmalik P, from Aix-les-Bains in eastern France.
It is not known whether this is the second attacker, whose face was badly disfigured by the police shooting.
Le Monde reports (in French) that Abdelmalik P strongly resembles a man already being sought by security services over fears he was about to carry out an attack.
The authorities have carried out DNA tests on the body of the second attacker.
The video released by IS shows two men speaking in Arabic and referring to IS leader Abu Bakr al-Baghdadi. One holds a piece of paper on which the IS flag is printed.
It was posted by the Amaq news agency, the media arm of IS, and has not been verified by French police.
Reports on Tuesday said the men had filmed the attack, but it is not clear where the video posted by Amaq was recorded.
The killing in Normandy came 12 days after the lorry attack in Nice in which 84 people died. The Nice killer also pledged allegiance to IS.
Several top French media outlets have said they will stop publishing the names and images of attackers linked to IS to try to prevent them becoming glorified.
Earlier on Wednesday, French religious leaders called for more security at places of worship across the country.
Representatives of Christian, Muslim, Jewish and Buddhist faiths spoke after meeting President Francois Hollande.