The New York police department's surveillance of the city's Muslim community violates longstanding rules drawn up to prevent spying and harassment of political activists in the 1960s and 70s, according to a legal challenge filed on Monday.

Civil rights lawyers say such "widespread and intense" surveillance has created a climate of fear, and stigma among Muslims living in New York. They are now seeking a court injunction against the NYPD's ability to instigate investigations into Muslims without evidence of crimes and for a judge to appoint an independent monitor to oversee its counter-terrorism efforts.

Lawyers describe NYPD surveillance of Muslims – first revealed by an Associated Press investigation – as an "all-encompassing dragnet" for intelligence, based on the false assumption that "conservative Muslim beliefs and participation in Muslim organisations are themselves bases for investigation."

They cite a series of AP reports about a small counter-terrorism unit within the investigations department, known as the Demographics Unit, later the Zone Assessment Unit, dedicated to infiltrating Muslims in Greater New York. The lawyers said NYPD officers used intrusive methods to routinely monitor restaurants, bookstores and mosques, and created dossiers of innocent conversations without any evidence of criminal activity.

The NYPD has also sent paid infiltrators into mosques, student associations and beyond to take photos, write down license plate numbers and keep notes on people for no reason other than their faith.

"Investigations of any community that are not based upon indications of crime create fear, and erode the confidence of a community in the power of a legal system to protect it," said Paul Chevigny, a professor of law at New York University and one of five attorneys on the case.

"We brought this motion because even in the face of the startling evidence in the press reports, Commissioner Kelly and Mayor Bloomberg have declared the NYPD will continue its intrusive secret surveillance program targeting completely innocent activities in Muslim communities, notwithstanding the prohibitions in the Handschu guidelines the NYPD is obliged to follow."

The Handschu guidelines, named after Barbara Handschu, the plaintiff in a lawsuit over similar widespread harassment of anti-war protesters by the police's so-called Red Squad in the 1960s, were imposed as part of a landmark settlement in 1985. The case was settled with the imposition of the Handschu guidelines, which prohibited investigations of political and religious organizations unless there was "specific information" that the group was linked to past or present crime.

Shamiur Rahman, a former NYPD infiltrator, was paid as much as $1,500 a month to spy on the Muslim community. In a declaration filed as part of the motion, Rahman describes how he took photos of worshippers at mosques, took down cell phone numbers of those who had signed up for Islamic education classes, and provided images of Muslim students at John Jay College.

"My NYPD boss Steve told me that the NYPD did not think the John Jay Muslim Student Association was doing anything wrong, [and that] they just wanted to make sure," Rahman said. "The members of the MSA were religious Muslims, and according to Steve, the NYPD considers being a religious Muslim a terrorism indicator."

Lawyers involved in the long-running battle Handschu case successfully opposed a policy introduced by the NYPD after the 2004 Republican convention to video and conduct surveillance operations in the absence of unlawful activity.

When contacted by the Guardian, the NYPD did not immediately respond.

The NYPD and Michael Bloomberg have said the department follows the Handschu guidelines, and did not break any laws over the course of its surveillance of Muslim communities.

Supporters said the Demographics Unit was central to keeping the city safe, though a senior NYPD official testified last year that the unit never generated any leads or triggered a terrorism investigation, according to the Associated Press.

NYPD commissioner Ray Kelly has said the department has plenty of oversight, including five district attorneys, a committee that investigates police corruption and the NYPD's own internal affairs office.