New York's West Texas Intermediate (WTI) for May delivery dropped 28 cents to USD 101.30 a barrel in afternoon trade and Brent North Sea crude for May shed 13 cents to USD 107.63.
The Ukrainian defence ministry's general staff spokesman Oleksiy Dmytrashkivskiy told AFP that Russian forces have been "gradually withdrawing" from its border.
The United States said it would welcome any Russian move to pull its forces back, but did not confirm reports that Moscow had begun to do so.
"The tapering of the geopolitical tensions may have... reduced the risk premium that has previously been pegged to the oil prices," Kan told AFP.
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Russia provides about a quarter of Europe's natural gas supplies, with about 80 per cent of those exports travelling through pipelines in Ukraine.
Russian troops are massed on the borders of eastern Ukraine, sparking fears about Moscow's plans after its takeover of the Crimean peninsula last month.
The official purchasing managers index (PMI) was 50.3 in March, the National Bureau of Statistics said in a statement, up from an eight-month low of 50.2 in February.
The market had expected the PMI to remain unchanged in March, according to a poll of economists by Dow Jones Newswires.
A reading above 50 indicates growth, while anything below signals contraction.