The call was issued by the American Muslim Taskforce on Civil Rights and Elections - Political Action Committee.
The group said it had carefully considered overall US interests and the "Muslim constituency's cares and concerns" in reaching its decision.
AMT claimed to be an umbrella organization for a number of Muslim groups in the United States. It said there are an estimated 7 million Muslims in the United States who will be swing voters in the battleground states.
"The Bush Administration has been extremely insensitive to the civil liberties and human rights of American Muslims, Arabs, and South Asians," its news release said.
The group had been expected to endorse Ralph Nader but its statement only praised him for "highlighting the denial of civil liberties to religious and ethnic minorities."
While supporting the Kerry campaign, the group also said the campaign "has failed to affirm its support for due process, equal justice, and other constitutional norms."
Copyright 2004 by United Press International