Gov. Kathy Hochul of New York signed a bill on Monday intended to give the state’s health care providers an extra layer of protection to shield them from prosecution in states that ban abortion.

The newly signed law comes days after a New York doctor was indicted in Louisiana for prescribing and sending abortion pills to someone in the state. The charges represented an escalation in the fractious battle between mostly Republican-led states that ban abortion and Democratic-led states seeking to protect or expand abortion access.

The law, which takes effect immediately, will allow health-care practitioners to avoid putting their names on prescriptions for medications used in abortions, and instead use the names of their medical practices.

Ms. Hochul, a Democrat, said the goal was to better conceal the identity of providers in hopes of protecting them from criminal, civil or other legal action that anti-abortion states try to take against them.

“Other states want to target, harass, scare, intimidate doctors and patients. That may be OK in a place like Louisiana — maybe Indiana,” Ms. Hochul said at a news conference on Monday. “But those are not our values here in the state of New York.”

The legislation signed on Monday augments the state’s telemedicine abortion shield law, under which New York authorities are barred from cooperating with a prosecution or other action taken by another state against a New York abortion provider.