(Updates with Russian report of the conversation)
By Steve Holland
RIYADH, March 28 (Reuters) - Russian President Vladimir Putin called U.S. President Barack Obama on Friday to discuss a U.S. diplomatic proposal for Ukraine, the White House said, adding that Obama told him that Russia must pull back its troops and not move deeper into Ukraine.
The Kremlin also reported on the conversation, saying Putin had suggested "examining possible steps the global community can take to help stabilize the situation," and said the foreign ministers of the two countries would discuss this soon.
It was believed to have been the first direct conversation between Obama and Putin since the United States and its European allies began imposing sanctions on Putin's inner circle and threatened to penalize key sectors of Russia's economy.
Russia's reinforcement of troops near Ukraine has brought the total forces there to as many as 40,000, U.S. officials estimated on Friday in a build-up that has increasingly worried Washington in recent days.
The White House noted specifically that it was Putin who called Obama, who is ending a four-country trip in Saudi Arabia and had just returned to his Riyadh hotel after talks with King Abdullah.
Putin called to discuss a U.S. proposal for a diplomatic resolution to the Ukraine crisis, which Secretary of State John Kerry again presented to Russian Foreign Minister Sergei Lavrov at a meeting at The Hague earlier this week.
The United States has been pressing Russia to pull back its troops to their Crimean bases and agree to talks with the Ukrainian government with international mediation. International monitors would go into Ukraine to assure that the ethnic Russian minority there is safe.
"President Obama suggested that Russia put a concrete response in writing and the presidents agreed that Kerry and Lavrov would meet to discuss next steps," the White House said.
In a statement posted on its website, the Kremlin said that Putin had cited the Russian justification for its actions toward Ukraine, which has centered on concern for Russian speakers there since the overthrow in February of Ukraine's pro-Russian president.
It said Putin "drew Barack Obama's attention to continued rampage of extremists who are committing acts of intimidation towards peaceful residents, government authorities and law enforcement agencies in various regions and in Kiev with impunity."
It was in light of this, it said, that the Russian leader had proposed actions by "the global community" to restore stability.
"FRANK AND DIRECT" TALKS
A senior Obama administration official described the call as "frank and direct," and said the next step was proposed talks between Kerry and Lavrov to see whether the Russians are serious about diplomacy.
The official also said Obama and Putin discussed the latest version of a "working document" that Kerry and Lavrov have been working on regarding ways to defuse the crisis.
"We have been in close touch with the Ukrainian government in this process," the official added.
Obama and European leaders this week piled pressure on Russia to de-escalate the Ukraine crisis in a peaceful way. In a speech on Wednesday in Brussels, Obama built his case for sanctions against parts of the Russian economy such as the energy industry and said NATO would bolster its presence in the alliance's member nations close to Russia.
The White House said Obama stressed to Putin that the United States continues to support a diplomatic path in close consultation with the Ukrainian government.
"President Obama made clear that this remains possible only if Russia pulls back its troops and does not take any steps to further violate Ukraine's territorial integrity and sovereignty," the White House said.
The Russian deployments on the border with Ukraine include the establishment of supply lines and the fielding of a wide range of military forces, U.S. officials said, speaking on condition of anonymity.
These include militia or special forces units made up of Russian fighters wearing uniforms lacking insignia or other identifying markings, similar to the first Russian forces to move into Crimea during Russia's recent military takeover there, according to U.S. and European sources familiar with official reporting.
Putin also raised Moscow's concern over conditions for largely Russian-speaking people in Transdniestria, a separatist region of Moldova to the west of Ukraine, whose leader has called for the territory to be annexed by Russia.
The statement said the people of Transdniestria were "essentially experiencing a blockade ... impeding their movement and normal trade and economic activities."
It said that "Russia stands for the fair and comprehensive settlement" of the conflict.
The speaker of Transdniestria's separatist parliament, during a trip to Moscow earlier this month, urged Russia to incorporate his region, which split away from Moldova in 1990.
The Kremlin statement was posted on the internet at http://eng.kremlin.ru/news/6936. (Reporting by Steve Holland and Steve Gutterman; Editing by by Alistair Bell, David Storey and Ken Wills)