"Crimea was TAKEN by Russia during the Obama Administration. Was Obama too soft on Russia?" the US president tweeted.
It comes as Russia insisted it did not intend to return Crimea to Ukraine after the White House said Mr Trump expected the annexed Black Sea peninsula to be returned.
Moscow said an overwhelming majority of Crimeans voted to become part of Russia in a 2014 referendum wanting protection from what the Kremlin cast as an illegal coup in Kiev.
However, Ukraine says the referendum was a sham held at gunpoint after Russian troops illegally annexed the peninsula, that Russia-friendly president Viktor Yanukovych was ousted by people power, and that Moscow should return Crimea.
"We don't give back our own territory. Crimea is territory belonging to the Russian Federation," Maria Zakharova, spokeswoman for the Russian Foreign Ministry, told a news briefing on Wednesday.
The 2014 annexation prompted the United States and the European Union to impose sanctions on Russia, plunging Western relations with the Kremlin to their worst level since the Cold War.
White House spokesman Sean Spicer said Mr Trump expected and wanted to get along with Russia, but was expecting Moscow to hand Crimea back.
Mr Trump's statements contradicts comments he made in an interview with ABC anchor George Stephanopoulos last year, when he said: “The people of Crimea, from what I've heard, would rather be with Russia than where they were."
The controversial orders Donald Trump has already issued
He also accused the "fake news media" of going "crazy" with "conspiracy theories and blind hatred".
Mr Trump went on to say to call intelligence agencies "very un-American!" and alleged they were giving out illegally giving out classified information "like candy".
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