President Trump announced Friday that he is pulling the U.S. out of its Intermediate-Range Nuclear Forces Treaty with Russia, saying Moscow has been cheating for years on the 1987 pact.

“The United States has fully adhered to the INF Treaty for more than 30 years, but we will not remain constrained by its terms while Russia misrepresents its actions,” Mr. Trump said in a statement. “We cannot be the only country in the world unilaterally bound by this treaty, or any other.”

He said the withdrawal will be completed in six months unless Russia comes back into compliance by destroying all of its violating missiles, launchers and associated equipment.

NATO said it “fully supports” Mr. Trump’s move. NATO Secretary General Jens Stoltenberg said Russia “is in material breach” of the INF Treaty and must use the next six months to return to full, verifiable compliance “or bear sole responsibility for its demise.”

Mr. Trump said the U.S. stands ready “to engage with Russia on arms control negotiations that meet these criteria, and, importantly, once that is done, develop, perhaps for the first time ever, an outstanding relationship on economic, trade, political, and military levels.”

“This would be a fantastic thing for Russia and the United States, and would also be great for the world,” he said.

Secretary of State Mike Pompeo said the withdrawal was justified because “Russia has jeopardized the United States’ security interests” by deploying a particular missile system in Europe.

The treaty, which had prohibited the U.S. and Russia from building or deploying land-based missiles and launch systems with a range of 300 to 3,400 miles, was designed to block the spread of so-called “tactical nukes” around the globe, particularly in Europe, partly out of fear the less powerful bombs were more likely to be used in an actual shooting war.

U.S. officials since 2014 have accused Moscow of breaching the INF, specifically through the deployment of a cruise missile known as the Novator 9M729.

“We can no longer be restricted by the treaty while Russia shamelessly violates it,” Mr. Pompeo told reporters at the State Department Friday morning.

“Russia’s violations put millions of Europeans and Americans at greater risk,” he said. “It is our duty to respond appropriately.”

“Countries must be held accountable when they break the rules,” Mr. Pompeo added.

Russia has acknowledged the 9M729 system’s existence but has claimed it does not violate the treaty.

The six-month period before the U.S. fully pulls out of the treaty is “Russia’s final chance” to restore the commitment, according to a senior administration official.

“Russia continues to deny its violation,” the official said Friday, and “is the one that has created a threat that exists that we successfully ended about 30 years ago.”

“We cannot be the only country bound by a treaty,” the official told reporters. “What purpose does it serve for the U.S. to be unilaterally bound to the treaty?”

The six-month waiting period is standard for most international treaties. It is intended to give other parties a final opportunity to restore its commitment.

“For [Russian President Vladimir] Putin this is very much about his neighbors, China being one of them,” the senior administration official said. “For the United States, this is strictly about the threat this poses to arms control.”

China and Iran are not bound by the INF treaty. Each country has thousands of the missiles in dispute and banned by the existing treaty.

Analysts say China, particularly, has developed large numbers of missiles that would violate the treaty, including the so-called DF-26 missile, informally dubbed the “Guam Killer.”

Republican Sen. James Risch of Idaho, chairman of the Senate Foreign Relations Committee, said he supports the move.

“I know that we have the unanimity of our allies in this decision, and we will continue to consult with them over the next six months as we approach the withdrawal date,” Mr. Risch said.

He said the treaty has become outdated and hasn’t stopped Russia from cheating.

“For the past several years, the Russian government has systematically violated the INF Treaty and deployed systems that undermine the stability that the treaty helped create,” he said. “Russian actions represent a material breach of the treaty, and it is abundantly clear: The United States is the only country limited by the INF Treaty.”

He said Moscow has had “endless opportunities to change their bad behavior” but has failed to do so.

“The time has come to set the treaty aside and develop alternative avenues toward the security the treaty once provided,” Mr. Risch said.

Some experts have argued that Russia developed the land-based missile because Moscow cannot compete with comparable U.S. sea- and air-based systems, which were not restricted by the treaty.

The decision was not a surprise to the Kremlin, which has claimed the Trump administration has long been determined to undermine the deal. Foreign Minister Dmitry Ryabkov, Russia’s top negotiator on the pact, denied again Friday that Russia had violated the terms of the INF and said Moscow was still willing to abide by its terms despite the U.S. withdrawal.

“We believe that the treaty is needed. It serves the interests of our security and European security,” Mr. Ryabkov said in an interview broadcast Friday, the Agence France-Presse news service reported. “It would be extremely irresponsible to undermine it with unilateral steps.”

He also accused the Trump administration of using the rejection of the treaty as a way to bleed Russia financially.

“They are probably beginning [an arms] race to exhaust us economically,” Mr. Ryabkov said.

Washington and Moscow also are discussing a possible extension of the START nuclear treaty for five more years. That agreement, which took effect in 2011, seeks to limit the size of the U.S. and Russian nuclear arsenals.

Some experts believe that Mr. Trump’s announcement about the INF Treaty means that the START pact could be ended as well.

A senior administration official said the U.S. has “not made any decisions about its extension.”

“We’re in the middle of an interagency process to evaluate our options,” the official said of START. “We are presently dealing with the Russians on this. We are working through some implementation challenges with them.”

• David R. Sands and Guy Taylor contributed to this story.