Obama took the call on a visit to Saudi Arabia and sources close to the White House say that it could lead to a Russian troop withdrawal in the region and the insertion of monitors to protect the rights of Russian speakers in Crimea.
Yesterday, Russia said it had "no intention" of invading eastern Ukraine, signalling Obama's bid not to be drawn into a new Cold War has for now, succeeded.
Russian foreign minister Sergei Lavrov reinforced a message from Putin that Russia would settle for control over Crimea despite massing thousands of troops near Ukraine's eastern border.
"We have absolutely no intention of - or interest in - crossing Ukraine's borders," Lavrov said.
The breakthrough came after a largely symbolic gesture at the United Nations General Assembly which passed a resolution recognising Ukraine's territorial integrity and describing as "illegal" the referendum that led to Russia's annexation of the Crimean peninsula. The resolution was supported by 100 countries with 11 opposed and 58 abstentions.
The "yes" vote counts for nothing other than to highlight the extent of international opposition to the Russian intervention. There will be no move within the more powerful 15-member Security Council for the reason that it will be vetoed by Russia, one of the five permanent members.
Following the vote, Ukraine's foreign minister Andriy Deshchytsia told the UN that his country's territorial integrity had been "ruthlessly trampled" in direct violation of the UN Charter. In response, Russia's UN Ambassador, Vitaly Churkin, claimed that a historic injustice in Crimea had been corrected by allowing its people to express their right to self-determination.
Both sides feel that they have right on their side but the danger lies in the fact that the quarrel is not just confined to Russia and Ukraine. As the UN vote showed it is in danger of drawing in the US and its European allies in the Nato alliance.
Meanwhile, a bid for regional devolution within Crimea is on the cards. Its Tatar community, an indigenous minority who were persecuted under Soviet rule, want autonomy. Yesterday, addressing 200 delegates at the top Crimean Tatars' assembly, Refat Chubarov, the Tatars' leader, said: "In the life of every nation there comes a time when it must make decisions that will determine its future."
Ever since the end of the Cold War Russia has had to contend with the steady encroachment of Nato eastwards as former Warsaw Pact allies such as Poland, Hungary and the Baltic states joined the alliance thereby extending the West's boundaries right up to Russia's doorstep. Although Moscow was offered the Partnership for Peace initiative in 1994 which embraces 22 former Soviet countries, Nato's steady expansion has always been viewed as a threat to national security.
When Ukraine signalled its intention in November last year of seeking a closer relationship with the European Union, this was seen as a first step towards complete integration into Europe and one which has to be resisted. If that happens, argue Russian diplomats, Nato will have a border with their country and one which cannot be easily defended.
Viewed from a Russian perspective, Nato's moves are not regarded as a post-Cold War settlement but as part of an aggressive policy which has taken advantage of Russia's perceived weakness. This gave President Vladimir Putin the pretext to intervene in Ukraine when Russian interests seemed to be threatened by the internal anarchy following the demise of president Viktor Yanukovych last month. Putin also realised that he had to act quickly, forcing the issue for a Crimean referendum before the west could offer any tangible response.
"Expanding Nato further into post-Soviet space is a red line with Russia, and the US is frankly not in a position to challenge it without running a huge risk," explained Greg Scoblete at the Real Clear World think tank. "Put bluntly, Russia will be able to invade eastern Ukraine faster than the West could admit Ukraine into Nato to deter Russian aggression."
According to Nato's secretary-general Anders Fogh Rasmussen, the possibility of Russia invading Ukraine is not an idle fear but a strategic reality which threatens European security. Once Russia had annexed Crimea it makes sense for them to consolidate their power by moving into eastern Ukraine to provide a buffer zone against further Nato encroachment. "Our concern is that Russia won't stop here," Rasmussen said last Wednesday. "There is a clear risk that Russia will go beyond Crimea and the next goal will be the eastern provinces of Ukraine."
The main check on these ambitions is Russia's faltering domestic economy. It cannot afford a lengthy confrontation with the West and lacks the military capacity to turn threats into a confrontation they have little hope of winning. A new arms race would be as ruinous for Putin as it would be for the rest of Europe.
Now into his second term in office, the last thing needed by President Barack Obama was a fresh international crisis. He was badly wrong-footed during the recent emergency in Syria when moves to mount punishment attacks were blocked by Russia's intervention, and this led to a growing perception that he was only capable of offering tepid leadership compared to Putin's macho approach to international affairs. Ukraine has done nothing to reset that opinion.
In moves that were only symbolic Obama ordered the despatch of small US navy and air forces to eastern Europe but the hard facts are that he has no stomach for a lengthy confrontation with the Russians. There will be a continuation of the so-called "smart" sanctions to target individual Russians and to make life difficult for their business activities. There may even be some repositioning of US forces within Europe but Obama has little interest in what is happening in Ukraine other than as a crisis which is impinging on US relations with Russia. It has not gone unnoticed in Washington that the decision to remove Russia from the G8 nations did nothing to stop Putin pushing ahead with his planned annexation of Crimea.
In his most recent comments on US television on Friday, Obama told Russia to pull back its forces from the border with Ukraine but he stopped short of issuing any specific warning about stopping the military build-up. As ever in his relationship with Putin, he managed to sound surprisingly conciliatory about Russia's intentions.
"There's a strong sense of Russian nationalism and a sense that somehow the West has taken advantage of Russia in the past," he said. "What I have repeatedly said is that he may be entirely misreading the West. He's certainly misreading American foreign policy."
In any case, Obama knows that he cannot deal with the problem in isolation. The US is dependent on Russian support in pushing through a deal with Iran to curtail that country's nuclear ambitions. In Syria, Russia is crucial to moves to keep president Bashar al-Assad on-side and to ensure the destruction of Syria's stockpile of chemical weapons. Looking ahead to autumn, Russia is an essential part of the jigsaw being constructed to extricate the US and its Nato allies from Afghanistan, providing the first staging post for the removal of personnel and equipment through the former Soviet Asian republics. This has the added benefit of avoiding the dangerous alternative route through Pakistan
That is not all: since the end of the Cold War, relations with Russia have become so normalised that any disruption of them will have an impact across the diplomatic and economic spectrum. That accounts for Obama's willingness to speak to Putin on Friday night. As a US diplomatic source put it: "Add on ongoing commitments such as the international space station which is manned by Russian and American crews and you can see that these interlocking agreements mean that we have to work together and avoid unnecessary tensions."
It is also fair to point out that Europe does not feature prominently in current US defence thinking. A recent State Department directive, entitled "Sustaining US Global Leadership: Priorities for 21st Century Defense", which outlines American strategic imperatives, there are few mentions of European affairs apart from a single paragraph devoted to Europe and Nato, neither of which are mentioned in Obama's foreword to the document.
Neither is there any reference to future Nato enlargement within Europe.