LOS ANGELES — About 200 people walked out of a meeting by a federal government task force Monday in protest over a program that gives immigration officials access to the fingerprints of arrestees.

The Department of Homeland Security assembled a group of law enforcement and community leaders

to make recommendations on ways to improve the so-called Secure Communities program, which gives immigration authorities access to the fingerprints of people who are arrested.

After a speaker challenged the two task force members leading the session to resign in protest, about 200 immigrant advocates got up and left, urging the public to follow. Many carried signs that read “Terminate Secure Communities” and flags from a number of countries including Mexico and Brazil.

“We have an opportunity to provide a recommendation,” retired Sacramento police chief Arturo Venegas, a task force member, told the boisterous crowd as they walked out.

About 50 people remained and a smaller, quieter meeting continued.

The meeting was aimed at getting public input on the program at a time when a number of states — including Illinois and Massachusetts — have said they want nothing to do with it.

Isaura Garcia fighting back tears, pleaded with the task force to help end the program.

Garcia, 20, said she called police after an episode of domestic violence to seek help finding a shelter for herself and her 1-year-old daughter, but instead wound up detained and was put into deportation proceedings.

“Calling 911 was the worst nightmare I could suffer in my life,” she said in Spanish.

The meeting was one of the first public discussions of Secure Communities since Immigration and Customs Enforcement on Aug. 5 terminated agreements signed with states to operate the program and said that state approval isn’t required to share fingerprints.

The program touted by immigration authorities as an information-sharing effort has become a headache for the Obama administration, which has plowed ahead with it despite vocal opposition from Latino and immigrant rights groups the president counts on for support.

Immigrant advocates say the program sends immigrants arrested for investigation of minor violations to jail and erodes their trust in police. They have also criticized the administration for giving the impression that local governments could choose whether to participate when it is in fact mandatory.

On Monday, immigrant rights groups urged members of the task force to call on ICE to end the program and questioned whether any real change would come from the task force meetings held last week in Dallas and scheduled this week in Los Angeles and Chicago.

Immigrant advocates are planning to hold protests Tuesday against Secure Communities in cities across the country.

“It is undermining community-police relations across the country,” Marielena Hincapie, executive director of the National Immigration Law Center, told the task force members. “This is not about tweaking the program. It is not about simple modifications… Only terminating the program will make a difference.”

Immigration and Customs Enforcement said in a statement that it has recently developed additional training for local law enforcement along with a new policy to protect domestic violence victims. ICE is running the program in 44 states and plans to achieve nationwide coverage in 2013.

Local law enforcement agencies routinely send fingerprints to the FBI for criminal background checks when an individual is arrested. Under Secure Communities, the FBI shares the fingerprints with Homeland Security to look for potentially deportable immigrants.

An ongoing source of debate is who is getting identified through this fingerprint sharing. Since 2008, about 121,000 immigrants have been deported after being flagged under Secure Communities, ICE statistics show.

About 6 percent had no prior record with immigration officials or law enforcement; roughly 28 percent had no criminal history, the statistics show.

That has led some immigrant advocates to clamor for changes, such as screening people after they are convicted of a crime instead of when they are arrested.

Groups in favor of stricter limits on immigration, such as the Washington-based Center for Immigration Studies, counter that it’s not feasible to wait for a conviction and the sole opportunity for consistent screening is during the booking process.

At Monday’s meeting in Los Angeles, several dozen of people spoke ardently against the program but a handful gave it praise.

“The only thing we are asking is to be secure,” said Julio Giron, 45, of Long Beach, while urging the task force to push for a tougher crackdown on illegal immigration.