WASHINGTON — The Justice Department escalated its promised crackdown on so-called sanctuary cities Tuesday, saying it will no longer award coveted grant money to cities unless they give federal immigration authorities access to jails and provide advance notice if someone in the country illegally is about to be released.

Under old rules, cities seeking grant money needed only to show they were not preventing local law enforcement from communicating with federal authorities about the immigration status of detainees.

Massachusetts municipalities including Amherst, Boston, Cambridge, Northampton, Salem, and Somerville have declared themselves sanctuary cities. And Monday, the state’s highest court ruled local law enforcement officials cannot hold a person who is wanted solely for immigration violations, providing a basis for cities to refuse to cooperate with US officials.

‘‘So-called ‘sanctuary’ policies make all of us less safe because they intentionally undermine our laws and protect illegal aliens who have committed crimes,’’ Attorney General Jeff Sessions said. ‘‘These policies also encourage illegal immigration and even human trafficking by perpetuating the lie that in certain cities, illegal aliens can live outside the law.’’

The rules affect a program that gives police money to buy everything from bulletproof vests to cameras. A judge in April blocked the presidents order withholding funding, saying he can’t set conditions on spending Congress had approved. But Justice said it still could condition some grants.