WASHINGTON—The State Department is adopting a new set of rules that will make it tougher for pregnant foreigners to visit the U.S. on tourist visas, an effort to prevent individuals from coming to the U.S. to give birth.

The new rules unveiled on Thursday, which take effect Friday, are aimed at cracking down on what the Trump administration calls “birth tourism.” They form another plank in the administration’s long-running effort to restrict access to the U.S., both to people looking to immigrate and others, particularly from...