President Joe Biden predicted on Friday that some U.S. states will try to arrest women for crossing state lines to get abortions after the Supreme Court overturned the constitutional right to the procedures nationwide.

Thirteen Republican-led states banned or severely restricted the procedure under so-called "trigger laws" after the court struck down the landmark 1973 Roe v. Wade ruling last week. Women in those states seeking an abortion may have to travel to states where it remains legal.

Convening a virtual meeting on abortion rights with Democratic state governors on Friday, Biden said he thinks "people are gonna be shocked when the first state ... tries to arrest a woman for crossing a state line to get health services."

He added: "And I don't think people believe that's gonna happen. But it's gonna happen, and it's gonna telegraph to the whole country that this is a gigantic deal that goes beyond; I mean, it affects all your basic rights."

Biden said the federal government will act to protect women who need to cross state lines to get an abortion and ensure their access to medication in states where it's banned.

New Mexico's governor, Michelle Lujan Grisham, told the meeting her state "will not cooperate" on any attempts to track down women who have had abortions to punish them. "We will not extradite," she said.