Angered by the U.S. Supreme Court decision to continue allowing private citizens to sue Texas abortion providers, Gov. Gavin Newsom of California on Saturday called for a similar law giving ordinary residents legal standing to file lawsuits against purveyors of restricted firearms.

“SCOTUS is letting private citizens in Texas sue to stop abortion?!” Mr. Newsom, a Democrat, tweeted. “If that’s the precedent, then we’ll let Californians sue those who put ghost guns and assault weapons on our streets. If TX can ban abortion and endanger lives, CA can ban deadly weapons of war and save lives.”

The governor’s response seemed to contradict his earlier criticism of the Texas law, which Mr. Newsom had previously described as a cynical attempt to undercut federal rights.

In a statement released on Saturday evening, Mr. Newsom said he had instructed his staff to work with California’s Legislature and attorney general to write a bill that would let citizens sue anyone who “manufactures, distributes, or sells an assault weapon or ghost gun kit or parts” in California. The governor called for damages of at least $10,000 per violation, plus costs and attorney’s fees.

“If the most efficient way to keep these devastating weapons off our streets is to add the threat of private lawsuits, we should do just that,” Mr. Newsom said in the statement.

The governor’s response seemed to explicitly position California opposite Texas in the divisive battles over abortion rights and gun control — and to position him personally on a national front in the culture wars.

Only three months ago, Mr. Newsom was locked in a bruising, Republican-led recall battle, which he beat back soundly. Relatively secure now in his prospects for re-election, the governor has increasingly raised his national profile. He has undertaken a national book tour to promote a children’s book he has written on dyslexia, a lifelong challenge. And as tornadoes swept through Southeastern states, leaving a path of devastation, Mr. Newsom publicly offered assistance to states such as Kentucky, deploying specialized urban search and rescue resources.

The governor’s vow to use California courts against gun violence followed the Supreme Court’s decision on Friday to let stand Texas’ ban on most abortions. The law allows private citizens to sue anyone who “aids or abets” an abortion performed after a fetal heartbeat can be detected. That development typically occurs around six weeks and often before women realize they are pregnant.

Supporters of abortion rights have criticized Texas for drafting its abortion ban to evade review in federal court, where it might be blocked. It effectively deputizes ordinary citizens, including those outside Texas, to sue clinics and others who violate the ban, awarding them at least $10,000 per illegal abortion if they are successful.

In a 5-4 decision led by the conservative majority, the Supreme Court ruled that abortion clinics could sue the state’s licensing officials to halt the new law, but could not sue state court judges, court clerks or the state attorney general. Otherwise, the court allowed the law, in effect since September, to stand.

As the Supreme Court has signaled that it might overturn Roe v. Wade, California political leaders have said they will work to make the state a refuge for women in parts of the country where abortion could be outlawed. Mr. Newsom’s response seemed to fulfill warnings that if the high court backed Texas’ legal strategy, liberal-leaning states might use the same tactic to limit rights dear to conservatives, such as gun rights.

The governor said that “if states can now shield their laws from review by the federal courts that compare assault weapons to Swiss Army knives, then California will use that authority to protect people’s lives, where Texas used it to put women in harm’s way.”

The reference was a swipe at a court ruling this year in which a federal judge overturned California’s three-decade-old ban on assault weapons, comparing the powerful guns, frequently used in mass shootings, to military pocketknives.