Putin calls Obama to discuss Ukraine
Mr Obama suggested that Russia put a concrete response in writing, his spokesman said in a statement.
Russia's annexation of Crimea has sparked international condemnation.
The US president urged Mr Putin to avoid the build-up of forces on the Russian border with Ukraine.
The White House said the two countries' foreign ministers would meet soon to discuss the next steps.
Mr Obama received Mr Putin's call in Saudi Arabia - the latest leg of a trip which also took the US president to Europe where the Ukraine crisis dominated discussions.
Meanwhile in New York, the UN Secretary General Ban Ki-moon said he had been assured by President Putin that the Russian leader "had no intention to make any military move".
Russia's reported troop movements near Ukraine's eastern border - described as a "huge military build-up" by Nato - has triggered fears that Mr Putin's interest in Ukraine is not limited to Crimea.
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