KIEV--Russia and the U.S. traded barbs Thursday over the presence of troops in Ukraine, a day after Washington said the Kremlin had resumed a buildup of forces around the conflict zone.

The stepped-up rhetoric comes amid signs of an unraveling of the agreement hammered out in Minsk to end the combat. While fighting was subdued on Thursday, Ukrainian troops and pro-Russian rebels have been exchanging fire near the eastern Ukraine cities of Donetsk and Mariupol for the past few days.

A buildup of Russian forces along Ukraine's border presaged heavy fighting inside Ukraine last year. On Wednesday, a State Department spokeswoman accused Russia of building up air defense systems inside eastern Ukraine, calling it "the highest amount of Russian air defense equipment in eastern Ukraine since August."

The spokeswoman, Marie Harf, said Russian troops were also taking part in training exercises with pro-Russian rebels in the area in violation of cease-fire accords, and that Russian forces were massing along the border inside Russia in the largest buildup since October.

The State Department said that Secretary John Kerry discussed Ukraine with Russian Foreign Minister Sergei Lavrov Wednesday and urged a withdrawal of Russian forces from Ukraine.

The State Department didn't report Mr. Lavrov's response, but Russia has repeatedly denied having troops in Ukraine.

On Thursday, Russian Defense Ministry spokesman Igor Konashenkov denied the latest State Department allegations as "strikingly incompetent." He accused the U.S. of sending troops into the combat zone, and said that it was training troops there near the eastern cities of Mariupol, Severodonetsk, Artyomovsk and Volnovakha.

Earlier this week, the U.S. formally began training Ukrainian troops at a base in western Ukraine near the Polish border. The U.S. denies having troops elsewhere in Ukraine, and on Thursday a Pentagon spokesman denied Mr. Konashenkov's claim, calling it a "ridiculous attempt to shift the focus" from Russia's own activities in the region.

"Russia continues to supply lethal weapons, training and command and control support for armed separatists in eastern Ukraine, in blatant violation of Moscow's Minsk commitments and Ukraine's sovereignty," said Eileen Lainez, a Pentagon spokeswoman.

The U.S. training program in western Ukraine involves about 300 U.S. troops who began work Monday with two elite units of Ukrainian Interior Ministry troops. The Kremlin has denounced it as a dangerous escalation in the conflict.

Write to Alan Cullison at alan.cullison@wsj.com

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