* US officials wary of Putin's assurances on Ukraine
* Kerry, Russia's Lavrov to meet again soon
* Obama says Putin grieving for loss of Soviet Union (Updates with Kerry-Lavrov meeting next week)
By Steve Holland and Jeff Mason
RIYADH, March 29 (Reuters) - U.S. President Barack Obama ended a four-nation foreign trip on Saturday in the same situation as he began it - facing great uncertainty about a diplomatic way out of the Ukraine crisis.
His diplomatic consultations in The Hague, Brussels and Rome over the past week all resulted in a strong show of unity between the United States and Europe that Russia must face consequences should it move against southern or eastern Ukraine.
But it remains an open question whether the European allies would be able to stomach the kind of crippling sanctions required to significantly undermine Russia's economy since some of their own economies would be jolted as well.
A late-night phone call on Friday between Obama and Russian President Vladimir Putin raised the possibility that Moscow might be willing to negotiate a diplomatic outcome.
But the news was greeted warily by U.S. officials, unconvinced that Putin really wants to cut a deal.
Obama talked to Putin just after a meeting in Riyadh with Saudi King Abdullah, where the civil war in Syria, another major bone of contention between the United States and Russia, was a main topic of conversation.
U.S. officials now will "see whether Russians are serious about diplomacy" on Ukraine, was how one senior Obama administration official described the aftermath of the phone call with Putin.
They recall all too well Russia's earlier assurances to the West that it would make no move against Ukraine's Crimea region - and then it annexed the Black Sea peninsula.
Now, U.S. officials are increasingly concerned about Russian troops, numbering as many as 40,000, massed on Ukraine's eastern border.
A Russian statement on the Putin-Obama phone call also said Putin had raised concerns about Transdniestria, a tiny breakaway territory comprised mainly of Russian-speakers in the ex-Soviet republic of Moldova.
At the heart of subsequent negotiations expected between U.S. Secretary of State John Kerry and Russian Foreign Minister Sergei Lavrov is a U.S. diplomatic "off ramp".
Under this plan, international monitors would be deployed to Ukraine to ensure the safety of ethnic Russians - the issue Moscow cited in annexing Crimea -, Russia would pull back its forces from the border and there would be a direct Russia-Ukraine dialogue.
Lavrov and Kerry discussed Ukraine in a telephone call on Saturday as well as the timing of further contact, Russia's Foreign Ministry said. Kerry will travel from Riyadh to Paris before a to-be-scheduled meeting with Lavrov early next week in Europe, State Department spokesman Jen Psaki told reporters.
U.S. officials are still puzzling over Putin's intentions. During a visit to The Hague, Obama said Russia was a "regional power" seeking to exert influence in the region.
"I think he's been willing to show a deeply held grievance about what he considers to be the loss of the Soviet Union," Obama told CBS News in an interview on Friday.
"I think there's a strong sense of Russian nationalism and a sense that somehow the West has taken advantage of Russia in the past and that he wants to in some fashion, you know, reverse that or make up for that."
Obama has not only to convince the Europeans of the need for strong action but also to explain to Americans back home why what happens in Ukraine should be of concern to the United States.
A recent CBS News poll showed 56 percent of Americans approve of sanctions enacted thus far by the United States and the European Union, but 65 percent do not think the United States should provide military aid and weapons to Ukraine.
The poll also showed 57 percent did not believe the United States had a responsibility to do something about Ukraine.
Obama himself said he could understand why people "might decide to look the other way", but that the "international order" must be protected. (Additional reporting by Lesley Wroughton in Shannon, Ireland, and Katya Golubkova in Moscow; Editing by Gareth Jones)