About 100 Muslim Americans marched to a city police station Tuesday to demonstrate their support for Officer Jesse Hartnett, who was shot last week, authorities said, by a man claiming to be an Islamic State supporter.

Waving signs saying that they backed police, Hartnett, and peace, the group - most in it students - denounced the shooting and terrorism.

"These are the real Muslims," said Ozzy Khalil, a spokesman for the Muslim American Society of Philadelphia, which operates a school, mosque, and community center near the Whitaker Avenue station house shared by the 24th and 25th Police Districts.

"We are neighbors, we support the Police Department, we help the police, and we pray for the speedy recovery of Officer Hartnett," said Khalil, who immigrated from the West Bank in 1991 and for years has worked with the districts' community organization.

Hartnett was shot three times in the left arm Thursday night near 60th and Spruce Streets. A police spokesman said Tuesday that he was in critical but stable condition.

Police quickly arrested Edward Archer, 30, of Yeadon. His mother said Archer had been "hearing voices" and needed medical help before the shooting. He was being held at the Curran-Fromhold Correctional Facility.

Local and federal investigators have been trying to determine if Archer had any link to terrorists.

Meanwhile, Mayor Kenney doubled down on his calls for viewing the ambush as the act of a disturbed man and not of a religion. In a Tuesday radio interview on WURD-AM, Kenney brushed off the criticism his stance has drawn from a Republican presidential candidate and a conservative radio icon.

"I mean, look who's criticizing me," Kenney said. "Marco Rubio and Rush Limbaugh. I'll take that any day of the week."

One of the people at Tuesday's rally was Saadiq Jabbar Garner, a member of the city's Commission on Human Relations. He praised participants.

Garner, who sometimes worships at the Muslim American Society's mosque on Luzerne Street, said the rally was intended to show that Philadelphia Muslims do not support terrorism.

Capt. Daniel O'Connor of the 24th District said the Muslim American Society, which is two blocks from his station house, had assisted police for years in a variety of neighborhood social projects.

As for terrorism, O'Connor said that "throughout history, all kinds of knuckleheads have done crazy things in the name of religion."

Inspector Michael McCarrick said the demonstration sent an important message about the strong relations between the department and the Muslim American organization.

McCarrick said he hoped the event would serve as a warning to "nitwits" who might consider retaliatory action against Muslims because of Hartnett's shooting.

mfazlollah@phillynews.com

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Staff writer Tricia L. Nadolny contributed to this article.