Mr. Putin suggested Russia might welcome a revival of multilateral talks on North Korea, known as the six-party negotiations, which have been dormant for a decade and were previously derided by Mr. Trump.

The Russian leader added that the United States and Russia have a common interest in preventing nuclear proliferation, in North Korea and elsewhere. But he also hinted at a longtime Russian argument that past American military action against governments at odds with the United States, like those of Iraq and Libya, made it hard today to persuade North Korea to disarm.

“The most important thing, as we have discussed today during the talks, is to restore the rule of international law and revert to the position where global developments were regulated by international law instead of the rule of the fist,” Mr. Putin said. “If this happens, this would be the first and critical step toward resolving challenging situations such as the one on the Korean Peninsula.”

Mr. Putin said Mr. Kim had asked him to share the details of the talks with the United States and China, saying there were “no secrets” at the negotiations.

Before they collapsed in 2009, the six-party talks among China, Japan, North Korea, South Korea, the United States and Russia had produced agreements to halt North Korea’s nuclear program, but the North later abrogated them.

Any Russian attempt to revive them now is bad news for Mr. Trump, who has repeatedly cited them as the prime example of the failed tactics of previous administrations. He has claimed that his own leader-to-leader diplomacy with Mr. Kim stood a far better chance of bringing about the North’s denuclearization.

Russian foreign policy has a different starting point. “In Moscow’s thinking, Kim Jong-un has learned from the fates of Iraq’s Saddam Hussein and Libya’s Col. Muammar el-Qaddafi that for an authoritarian regime, the only safeguard against U.S. military intervention is the possession of nuclear weapons capable of hitting the American mainland,” Aleksandr Gabuev, a fellow at the Moscow Carnegie Center, wrote.

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