In a statement, a coalition of Muslim leaders called Cahill’s remarks “bigoted … undignified” and “anti-democratic,” and said the governor has a right to meet with members of all religious backgrounds.

Last weekend, Patrick met with around 1,000 Massachusetts Muslim leaders who wanted to raise awareness about their faith and become more civically engaged.

“I fully support equal protection under the law for every American, regardless of race or creed, but this is political correctness run amok,” Cahill said after Patrick met with Muslim leaders.

Noting two Muslim Americans recently were arrested in Massachusetts in connection with the probe of the attempted Times Square bombing, Cahill added: “Gov. Patrick should stop playing politics with terrorism and focus on protecting all the citizens of this commonwealth.”

Cahill is the state Treasurer and former Democrat who has launched an independent campaign for governor.

“He is our governor and he has a right to meet with any religious organization,” said Kemal Bozkurt, publisher of the Lawrence-based Muslim Green Pages of New England, a directory of Muslim-owned businesses.

Bozkurt said if Cahill has any evidence that a mosque or Massachusetts Muslim group has terrorist ties he should turn it over to Attorney General Martha Coakley instead of stereotyping. “Those comments are unacceptable,” Bozkurt said. “Muslims must take action and not vote for a candidate like this.”

Sufia Hassan, a female leader and educator at the Mosque for the Praising of Allah in Boston, said remarks like those from politicians only give cover for some to “go after” Muslims.

“I feel as if myself and my children are being attacked,” said Hassan. “I was very offended.”

Hassan said Muslim Americans in Massachusetts would be worried if Cahill were elected governor but would still be open to working with him.