Yunadim Kanna, one of the few Christian members of parliament, said that a few hundred of those families had come back following signs that security had returned.
"The situation in these neighbourhoods is quiet now and under control," Kanna said.
A top official with the Displacement and Migration Ministry in Mosul, Jawdat Ismail, told Reuters at least 80 Christian families that had returned. He said Prime Minister Nuri al-Maliki was offering 1 million Iraqi dinars ($800) to each family to help them resettle, if they register.
The United Nations refugee agency put the number of Christian families who have fled Mosul at more than 2,200, and says some have taken refuge in neighbouring Syria.
The Christian exodus from Mosul, which was concentrated in the second and third weeks of October, began after around 12 Christians were reported killed. Others received death threats and several Christian homes were targeted in bomb attacks.
But many officials in Mosul, and the U.S. military, say that the number of confirmed attacks was small.
No one has claimed responsibility for the attacks in Mosul, where tensions between its Sunni Muslim Arab majority and a politically powerful Kurdish minority have been on the rise.
"So far we have no information about who was behind what happened there," Kanna said, calling the attacks a "well-organised operation."
He said a government probe into attacks on Christians had delivered its results to Maliki and that at least 10 people had been arrested.
Mosul is seen as one of the few remaining strongholds for Sunni Islamist al Qaeda despite years of assault from U.S. and Iraqi forces. U.S. intelligence say that at least a dozen different insurgent groups operate in the city.
(Reporting by Waleed Ibrahim; Writing by Tim Cocks; Editing by Dominic Evans)
- Reuters - Thomson Reuters Foundation
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