Militants in Iraq targeted Christians in two separate bomb attacks in Baghdad on Wednesday, killing at least 37 people, officials said.

In one attack, a car bomb went off near a church during Christmas Mass in the capital's southern Dora neighbourhood, killing at least 26 people and wounding 38, a police officer said.

Earlier in the day, a bomb ripped through an outdoor market in the nearby Christian section of Athorien, killing 11 people and wounding 21, the officer added.

There was no immediate claim of responsibility for the attacks, but Iraq's dwindling Christian community, which is estimated to number about 400,000 to 600,000 people, has often been targeted by al-Qaeda and other insurgents.

A medical official confirmed the casualty figures. Both officials spoke on condition of anonymity because they are not authorized to talk to the media.

Prime Minister Stephen Harper condemned the "senseless" attacks and offered condolences to family and friends of the victims.

“All forms of terrorism are unconscionable and immoral," Harper said in a statement. "However, acts of terror on innocent civilians at their place of worship on such a holy day are an abomination."

Wednesday's bombings came amid a massive military operation in Iraq's western desert as authorities try to hunt down insurgents who have stepped up attacks across Iraq in the past months, sending violence to levels not seen since 2008.

The Christmas Day attacks brought the total number of people killed so far this month in Iraq to 441. According to UN estimates, more than 8,000 people have been killed since the start of the year.