WASHINGTON — When officials from Russia and the United States sit down in Geneva on Monday for high-profile discussions with another war in Europe on the line, hovering over the talks will be an American diplomat who will not even be in the room.

Nearly 30 years after James A. Baker III stepped down as secretary of state, the current confrontation over Ukraine turns in part on a long-running argument about what, if any, commitments he made to Moscow in the waning days of the Cold War and whether the United States fulfilled them.

President Vladimir V. Putin and other Russian officials have asserted that Mr. Baker ruled out NATO expansion into Eastern Europe when he served as President George H.W. Bush’s top diplomat. The West’s failure to live up to that agreement, in this argument, is the real cause of the crisis now gripping Europe as Mr. Putin demands that NATO forswear membership for Ukraine as the price of calling off a potential invasion.

But the record suggests this is a selective account of what really happened, used to justify Russian aggression for years. While there was indeed discussion between Mr. Baker and the Soviet leader Mikhail S. Gorbachev in the months after the fall of the Berlin Wall about limiting NATO jurisdiction if East and West Germany were reunited, no such provision was included in the final treaty signed by the Americans, Europeans and Russians.

“The bottom line is, that’s a ridiculous argument,” Mr. Baker said in an interview in 2014, a few months after Russia seized Crimea and intervened in eastern Ukraine. “It is true that in the initial stages of negotiations I said ‘what if’ and then Gorbachev himself supported a solution that extended the border that included the German Democratic Republic,” or East Germany, within NATO. Since the Russians signed that treaty, he asked, how can they rely “on something I said a month or so before? It just doesn’t make sense.”

In fact, while Mr. Putin accuses the United States of breaking an agreement it never made, Russia has violated an agreement it actually did make with regard to Ukraine. In 1994, after the Soviet Union broke apart, Russia signed an accord along with the United States and Britain called the Budapest Memorandum, in which the newly independent Ukraine gave up 1,900 nuclear warheads in exchange for a commitment from Moscow “to respect the independence and sovereignty and the existing borders of Ukraine” and “to refrain from the threat or use of force” against the country.

Russia trampled Ukrainian sovereignty when it annexed Crimea and sponsored proxy forces to wage war against the Kyiv government in eastern Ukraine. And it is once again threatening the use of force by assembling 100,000 Russian troops along its border to extract guarantees that Ukraine will never be allowed to join NATO.

The dispute traces back to the final years of the Cold War, when East and West were negotiating the framework of what Mr. Bush would call the new world order. The fall of the Berlin Wall on Nov. 9, 1989, led to negotiations over unifying the two Germanys formed after World War II.

The Bush administration was determined to anchor a combined Germany within NATO, but Western officials sought to assuage the Soviets’ concerns about their security. On Jan. 31, 1990, Hans-Dietrich Genscher, the West German foreign minister, said in a speech that there would not be “an expansion of NATO territory to the east, in other words, closer to the borders of the Soviet Union.”

He was talking about whether NATO troops would be stationed in territory then constituting East Germany, not whether other countries would eventually be considered for membership in the alliance. Nonetheless, Mr. Baker picked up on Mr. Genscher’s formulation during a Feb. 9 visit to Moscow.

As an inducement for agreeing to German unification, Mr. Baker offered what he called “ironclad guarantees that NATO’s jurisdiction or forces would not move eastward,” according to a declassified memorandum recording the discussion.

“There would be no extension of NATO’s jurisdiction for forces of NATO one inch to the east,” Mr. Baker told Mr. Gorbachev, coming back to the formula three times during the conversation.

Back in Washington, the National Security Council staff was alarmed. The word “jurisdiction” could imply that the NATO doctrine of collective defense would apply only to part of German territory, limiting German sovereignty. It was one thing to agree not to move troops into the East right away, as far as American officials were concerned, but all of Germany had to be part of NATO.

“The N.S.C. got to him pretty quickly and said that language might be misinterpreted,” Condoleezza Rice, then a Soviet adviser to Mr. Bush and later secretary of state under President George W. Bush, remembered in an interview for a biography of Mr. Baker.

Mr. Baker got the message and began walking back his words by ditching the term “jurisdiction” from all future discussions. Chancellor Helmut Kohl of West Germany likewise rejected Mr. Genscher’s formulation.

“I may have been a little bit forward on my skis on that, but they changed it and he knew that they changed it,” Mr. Baker recalled of Mr. Gorbachev. “He never once again in all the months that followed ever raised the question of NATO expanding its jurisdiction eastward. He then signed documents in which NATO did expand its jurisdiction.”

When Mr. Baker returned to Moscow in May, he offered what were called the nine reassurances, including a commitment to allow Soviet troops in East Germany to remain for a transition period and not extend NATO forces into that territory until they left. This was hardly a promise not to extend the alliance east, but he insisted to the Soviets that this was the best the United States could do.

Mr. Gorbachev eventually agreed. The final treaty unifying Germany later in 1990 barred foreign troops from the old East Germany, but German troops assigned to NATO could be deployed there once Soviet forces withdrew by the end of 1994. Nothing in the treaty addressed NATO expansion beyond that.

“Now remember, it’s not clear the Soviet Union is going to collapse at this point,” Dr. Rice recalled. “It’s not even clear that the Warsaw Pact is going to collapse. This is about the unification of Germany.” She added, “The expansion of NATO was just not on the table as an issue in ’90-’91.”

No less a witness agreed than Mr. Gorbachev. “The topic of ‘NATO expansion’ was not discussed at all, and it wasn’t brought up in those years,” he told an interviewer after Russia’s intervention in Ukraine seven years ago. The issue was foreign troops in eastern Germany. “Baker’s statement” about not one inch “was made in that context,” Mr. Gorbachev said. “Everything that could have been and needed to be done to solidify that political obligation was done. And fulfilled.”

Having said that, Mr. Gorbachev agreed that NATO expansion was unnecessarily provocative. “It was definitely a violation of the spirit of the statements and assurances made to us in 1990,” he said.

As it happens, one of those who suggested a different approach was Mr. Baker. In 1993, as NATO was contemplating admitting Poland, Hungary and the Czech Republic, he proposed in an op-ed in The Los Angeles Times that the alliance consider another possible member: Russia itself.

The idea would be to force democratic change before it could join, while making clear that Russia was not an enemy. “For our relations with Russia, it can both encourage reform and hedge our bets against a return to authoritarianism and expansionism,” Mr. Baker wrote. That obviously never happened.