• The group, which has five seats in Iraq's parliament, filed a lawsuit saying it was undemocratic.
• Public alcohol consumption is frowned upon in Iraq, a predominantly Muslim country, but it can be bought at liquor stores or licensed bars.
Christian politicians in Iraq are attempting to overturn legislation banning the import and sale of alcohol.
Customs officials were given orders on Saturday to enforce the ban. It became law last month despite opposition.
The group, which has five seats in Iraq's parliament, filed a lawsuit saying it was undemocratic.
Public alcohol consumption is frowned upon in Iraq, a predominantly Muslim country, but it can be bought at liquor stores or licensed bars.
The law, originally passed by parliament in 2016, imposes a fine of up to 25m Iraqi dinars (£14,256).
It prohibits the sale, import or production of alcohol - and only became official last month, seven years since it was passed, after appearing in the official gazette.
It remains unclear how strictly the law could be enforced, and whether the country's Federal Supreme Court will knock it back.
In their appeal to the court, members of the Babylon Movement insisted the legislation was unconstitutional because it ignores the rights of minorities and restricts freedom.
It also contradicts a government decree, adopted less than a week before the gazette was published on 20 February, setting duty at 200% on all imported alcoholic drinks for the next four years, they say.
Sarmad Abbas, an estate agent based in Iraq's capital Baghdad, told the AFP news agency that the ban would merely push alcohol sales onto the black market.
He acknowledged that Muslim teachings forbid the consumption of alcohol. "But these are personal freedoms that you cannot forbid citizens from practising," he said.
According to reports at the time, the bill was originally proposed by Mahmoud al-Hassan, then a judge and lawmaker for Iraq's State of Law Coalition.
He said it was in keeping with Article 2 of Iraq's 2005 constitution, which prohibits any legislation that goes against Islam, the AP news agency wrote.