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Accounts of an impending American-Russian presidential meeting have been greatly exaggerated, it seems.

Only a few days after President Trump said he intended to confer with Russia's leader Vladimir Putin in Budapest - "within two weeks or so" - the summit has been put off without a new date.

A initial get-together by the two nations' top diplomats has been cancelled, too.

"I prefer not to have a wasted meeting," Donald Trump told reporters at the executive mansion on Tuesday afternoon. "I don't want a pointless effort, so I'll see what happens."

• Trump says he did not want a 'unproductive session' after arrangement for negotiations with Putin postponed
• Letdown in Ukraine's capital as Zelensky leaves White House empty-handed

The on-again, off-again summit is just the latest twist in the president's efforts to mediate an end to hostilities in Ukraine – a subject of renewed focus for the US president after he arranged a truce and hostage release deal in Gaza.

While making remarks in Egypt recently to commemorate that truce deal, the president turned to his lead diplomatic negotiator, with a fresh directive.

"We have to get Russia resolved," he said.

However, the circumstances that converged to make a Gaza breakthrough possible for the negotiation team may be difficult to duplicate in a conflict in Ukraine that has been ongoing for nearing four years.

Less Leverage

According to the lead negotiator, the crucial element to unlocking a deal was the Israeli government's move to strike representatives of Hamas in the Gulf state. It was a move that angered America's Arab allies but gave the president leverage to compel Israel's leader Benjamin Netanyahu into making a deal.

Trump gained from a history of supporting Israel dating back to his initial presidency, encompassing his decision to move the American embassy to Jerusalem, to alter America's position on the legality of Israeli settlements in the West Bank and, in recent times, his support for Israeli defense operations against the Islamic Republic.

The American leader, actually, is better regarded among Israelis than Netanyahu – a position that provided him with unique influence over the nation's head.

Add in Trump's political and economic ties to influential Arab nations in the region, and he had a abundant diplomatic muscle to force an deal.

In the Ukraine war, by contrast, the president has significantly reduced influence. Over the past nine months, he has swung between efforts to pressure the Russian president and then Zelensky, all with little seeming effect.

The US leader has warned to impose new sanctions on Russia's oil and gas sales and to supply the Ukrainian forces with new long-range weapons. But he has also acknowledged that such actions could harm the world's financial stability and further escalate the conflict.

At the same time, the US leader has criticized openly Ukraine's president, temporarily cutting off intelligence-sharing with Ukraine and suspending weapon deliveries to the nation - only to then retreat in the face of concerned European allies who caution a Ukrainian collapse could destabilise the whole area.

The president often boasts about his skill to sit down and negotiate agreements, but his personal discussions with the Russian and Ukrainian leaders have not appeared to move the war any closer to a peaceful end.

Putin may actually be exploiting Trump's desire for a deal – and belief in direct negotiations - as a means of influencing him.

In July, Russia's leader consented to a summit in Alaska at the time when it seemed probable that the president would approve on legislative penalties backed by Senate Republicans. That legislation was afterwards delayed.

Recently, as reports spread that the White House was considering seriously sending long-range missiles and Patriot anti-air batteries to Ukraine, the president of Russia phoned the US president who then promoted the potential meeting in Hungary.

The next day, the president hosted Zelensky at the White House, but departed without agreements after a allegedly strained discussion.

The US leader insisted that he was not being played by the Russian president.

"As you are aware, I've been played all my life by the best of them, and I came out really well," he said.

But the president of Ukraine later commented on the sequence of events.

"Once the matter of long-range mobility became a little further away for us – for Ukraine – Russia almost automatically became less engaged in negotiations," he said.

Thus, in a short period, the president has bounced from entertaining the prospect of sending missiles to the Eastern European country to planning a Budapest summit with Russia's leader and confidentially urging the Ukrainian president to surrender all of Donbas – even territory Russia has been unable to conquer.

He has finally settled on calling for a ceasefire along current battle lines – a proposal Russia has refused to accept.

On the campaign trail last year, Trump promised that he could end the Ukraine war in a very short time. He has since discarded that commitment, admitting that ending the war is turning out harder than he anticipated.

It has been a uncommon admission of the limits of his power – and the challenge of finding a framework for peace when neither side wants, or can afford to, give up the fight.