Tensions in the region remained high despite the release of a Ukrainian naval commander held by pro-Russian forces.
Shots were fired but there were no casualties as the Ukrainian corvette Khmelnitsky was seized in Sevastopol, according to an AP photographer at the scene. Another ship, the Lutsk, was also surrounded by pro-Russian forces. An AP photographer later saw Ukrainian servicemen disembarking a third ship, the Ternopil corvette.
Ukrainian Deputy Defense Minister Leonid Polyakov accused Russian troops of constantly threatening to storm military bases where Ukrainian soldiers were located, according to the Interfax news agency.
In Geneva, Ukraine's ambassador to the United Nations warned of a sharp deterioration in relations between the two neighbors, saying that Russia appears to be preparing for a military "invasion" in more areas of his country.
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Ambassador Yuri Klymenko said there were "indications that Russia is on its way to unleash a full-blown military invention in Ukraine's east and south" since its annexation of Crimea. He said his statement was based on information from non-governmental organizations.
Obama also warned of more costs to come for the Kremlin if the situation worsens, saying he also had signed an executive order that would allow the US to penalize key sectors of the Russian economy.
Within minutes of Obama's speech, Russia retaliated by banning entry to nine US officials and lawmakers.
Speaking after meeting with Putin in Moscow, UN Secretary-General Ban Ki-moon said he "emphasized that all parties refrain from any hasty or provocative actions that could further exacerbate an already very tense and very volatile situation.