Immigrants and immigration advocates asked the Boston City Council Monday to preserve the law that limits Boston police’s ability to cooperate with federal immigration authorities and also to strengthen the protection it provides.

The 2014 Trust Act, which Mayor Michelle Wu defended during a Congressional hearing in Washington, D.C., last week, helps immigrants feel safe in the city, speakers said during a council hearing. But under the current presidential administration, which has made immigration enforcement and deportations a priority, that protection is especially important.

“I’ve witnessed parents afraid of sending their children to school, worrying about what will happen if they step out of their homes,” said Nivia Pina, a Boston Public Schools teacher and small business owner. “The fear is harmful to our community, our workplaces and our schools. No one should have to live in fear simply for trying to build a better future for their family.”

• Read more: Boston’s Trust Act: What it is and how it works

The Trust Act prohibits local police from working with U.S. Immigration and Customs Enforcement on civil immigration enforcement efforts. Police officers are prohibited from asking people about their immigration status, making arrests or holding someone based on ICE administrative warrants if there is no other criminal charge or otherwise “performing the functions of an immigration officer.”

Boston police are still free to work with ICE on criminal investigations, including drug or human trafficking cases.

City officials and supporters of the law have said it protects public safety by allowing undocumented immigrants to contact law enforcement to report a crime or provide information for an investigation without the fear of being deported.

However, some of the advocates at the hearing, which was held to assess the effectiveness of the Trust Act in the decade since it was enacted, said those protections could be strengthened.

Policy consultant Neenah Estrella-Luna said that while the text of the law specifies that police can cooperate with ICE on investigations involving criminal charges or “aggravated felonies,” those terms can be left up to interpretation without more specific language.

“At the federal level, you will find that that law under aggravated felonies includes things like shoplifting. And I don’t know about you, but I do not define stealing bread or deodorant or baby formula as an aggravated felony,” Estrella-Luna said.

Suzanne Lee, an educator and retired Boston Public Schools principal, said the Trust Act is especially important for protecting children in schools. She said school staff need to be trained to know what to expect, because while typically they would not need to know the specifics of immigration law, right now, they do.

The fear of immigration enforcement, she said, is negatively affecting students, even those who are in the country legally.

“When children don’t feel safe and worry about their parents, and worry about whether or not when they get home their parents will be there, or whether or not they have jobs that can provide for them … They don’t focus. They tend to act out,” she said, adding that this affects other students in the classroom as well.

“You cannot learn unless you have the mental capacity to feel safe and then open your mind to learn,” she said.

While most people at the hearing supported the law, a few testified against it during the public comment period.

Shawn Nelson, a former City Council candidate who also attended a rally against the Trust Act in front of City Hall on the day of Wu’s Congressional testimony last week, accused city councilors of supporting the law to “push … the Democrats’ agenda.”

“You are not cooperating with the federal government with taking out illegal immigration,” Nelson said. “This has nothing to do with those who came here legally. You actually are disrespecting the hard work they had to go do to come into this country, to allow people to break our federal laws and to protect them.”