WASHINGTON — President Trump’s weekend announcement that he would pull the United States out of a key nuclear arms control treaty alarmed members of his own party, who criticized the decision and worried that other international pacts to control proliferation of the world’s most dangerous weapons also might be upended.

“I hope we’re not moving down the path to undo much of the nuclear arms control treaties that we have put in place,” Senate Foreign Relations Committee Chairman Sen. Bob Corker, R-Tenn., said Sunday on CNN’s “State of the Union,” noting that he had heard that the Trump administration wanted to pull out of not only the Intermediate-range Nuclear Forces, or INF, Treaty, but also New START.

“I think that would be a huge mistake,” Corker said.

Trump told reporters on Saturday night that his administration would “terminate” and “pull out” of the Intermediate-range Nuclear Forces Treaty, a strategic arms reduction pact that President Ronald Reagan and Soviet leader Mikhail Gorbachev struck in 1987. Russia has long been accused of violating the treaty, prompting calls from some defense hawks in the United States to end U.S. participation in the deal. Many also argue that the treaty is obsolete, because it doesn’t restrict China’s proliferation.

New STARTseeks to limit the stockpiles of long-range and submarine missiles and heavy bombers, plus related warheads and launchers, in U.S. and Russian possession. Corker played a leading role in helping the Senate ratify an updated extension of the treaty in 2010; but its future is in doubt, as it expires in early 2021.

Trump’s announcement came as his national security adviser, John Bolton, traveled to Russia to meet with counterparts and discuss, among other things, treaty compliance. But Corker said Trump’s announcement to pull out of the INF Treaty came as a surprise – and one he hoped was simply presidential bluster.

“This could be something that is just a precursor to try to get Russia to come into compliance,” Corker said, guessing that Trump might be attempting a power play to influence Russia’s stance on nuclear arms control treaties as he did with the parties to NAFTA to affect trade policy. But Corker warned that unless the United States was ready to compete with Russia, “they’re going to move ahead of us quickly.”

For the past few years, the annual defense authorization bill has funded research and development of weapons that, if ever tested, would violate the INF Treaty. The argument has been that the research is necessary to counter China’s aggressive moves in places such as the South China Sea, in the event that the treaty is renegotiated or declared null and void. China is not a party to the treaty.

Though it takes a two-thirds vote of Congress to ratify a treaty, there is no constitutionally mandated congressional role in tearing one up – leaving critical lawmakers, including one of the president’s staunchest defenders on foreign policy, Sen. Rand Paul, R-Ky., little recourse but to plead with Trump to pursue negotiations to update and broaden the INF Treaty instead of declaring it dead.

“It’s a big, big mistake to flippantly get out of this historic agreement,” Paul said on “Fox News Sunday.” “I’m all for trying to sign an agreement with China, but that would have to be a brand-new agreement. It’s no reason to end the agreement we have with Russia.”

Paul encouraged Trump to appoint nuclear negotiators to work on updating and expanding the pact, and “have a rational discussion with experts on this and see if we can resolve it.” But he insisted that Bolton play no part in that treaty discussion.

“John Bolton is the one advising the president to get out of the INF Treaty,” Paul said. “I don’t think he recognizes the important achievement of Reagan and Gorbachev on this.”