WASHINGTON, July 24 (Reuters) - The White House said it did not support Ukraine launching attacks inside Russia after two drones from Ukraine damaged buildings in Moscow earlier on Monday.

"As a general matter we do not support attacks inside of Russia," White House spokesperson Karine Jean-Pierre told reporters in a press briefing.

Russia vowed to take harsh retaliatory measures against Ukraine, calling the two drone strikes, including one close to the Defence Ministry's headquarters, a brazen act of terror.

"This is a war that Russia started. This is their war," Jean-Pierre said. "And they can end it at any time by withdrawing forces from Ukraine instead of launching brutal attacks on civilians."

Nobody was hurt in the attack in Moscow -- the most high-profile of its kind since two drones reached the Kremlin in May.

One drone struck close to Russia's defense headquarters in a symbolic blow that underscored the reach of such drones, and a senior Ukrainian official said there would be more attacks.

Meanwhile, Kyiv on Monday said a Russian drone attack destroyed Ukrainian grain warehouses on the Danube River and wounded seven people.

The Kremlin said it would press on with what it calls its "special military operation" in Ukraine. Kyiv and much of the West say is a brutal war of conquest.

A swarm of 17 drones also launched attacks overnight on Crimea, which Russia annexed from Ukraine in 2014, the Russian Defence Ministry said. They struck an ammunition warehouse and damaged a residential building, the Russian-installed head of Crimea said.