WASHINGTON — The Biden administration published new guidelines on Thursday for which undocumented immigrants should be prioritized for arrest, giving Immigration and Customs Enforcement agents broad discretion to decide who poses threats to public safety and national security. The priorities are intended to further undo the broad immigration arrest policies of the Trump administration, and to instead direct immigration officers to focus on each person rather than categories of specific offenses. "The fact that an individual is a removable noncitizen should not alone be the basis of an enforcement action against them," Alejandro N. Mayorkas, the secretary of homeland security, said on Thursday. "Therefore, we are requiring and, frankly, empowering our work force — critically, empowering our work force — to exercise their judgment, their law enforcement judgment." Such considerations include the seriousness of a past offense, what kind of harm it caused and whether a firearm was involved. Under the guidelines, agents should also consider "advanced or tender age" as a mitigating factor. Other considerations include the effect that arresting and eventually deporting someone would have on the person's family. But some immigration advocates think the guidelines give agents too much discretion without a clear plan for accountability. The guidelines come as Democrats appear to be losing a fight to include a path to citizenship for millions of unauthorized and temporarily authorized immigrants in a sprawling budget reconciliation bill. The new arrest priorities would largely exclude the noncitizens to whom lawmakers had hoped to extend permanent residency, including young adults who arrived in the country as children, as well as farm and health care workers. There are 11 million noncitizens in the country — some with temporary authorization to live and work, but many without any documentation at all — and limited resources to enforce the law. Early in his administration, President Donald J. Trump rejected the prosecutorial discretion his predecessor put in place on immigration enforcement and instead set out to arrest any noncitizen in the country without authorization, speed deportations and enlist local law enforcement more often to act as immigration enforcers. Mr. Trump's first press secretary, Sean Spicer, said the president wanted to "take the shackles" off Immigration and Customs Enforcement agents, which some agents at the time said was a welcome change. Lena Graber, a senior staff attorney at the Immigrant Legal Resource Center, said she worried that the guidelines gave officers so much discretion that enforcement actions would not look much different from those during the Trump administration.