An under construction Gurdwara in the American State of Michigan has been vandalised and defaced with anti-Muslim graffiti, the police and community leaders have said.

The vandalism of the Gurdwara, coming up in Sterling Heights city of Michigan, happened on February 5, members of its management committee said.

The graffiti included vulgar language, racial epithets, the use of what appears to be a cross, a large drawing of a gun, and references to the 9/11 attacks, the Sikh American Legal Defence and Education Fund said, urging the local and federal authorities to initiate a hate crime investigation into it.

The vandalism has been condemned by the Michigan chapters of the Council on American-Islamic Relations and the American Jewish Committee.

"We condemn the vandalism of the Sikh house of worship in Sterling Heights and call on local and federal law enforcement to use their full resources to apprehend the perpetrators of this hate crime," said Dawud Walid, executive director of the Muslim council.

"The attack on any house of worship in our community is despicable, and we are pained to see the Sikh community targeted," said Kari Alterman of the Jewish committee.