WASHINGTON (Reuters) - A Russian fighter aircraft made repeated low-altitude, close-range passes near a U.S. ship in the Black Sea over the weekend, the Pentagon said on Monday, condemning the action at a time of heightened U.S.-Russian tensions over Ukraine.

"This provocative and unprofessional Russian action is inconsistent with their national protocols and previous agreements on the professional interaction between our militaries," said Colonel Steve Warren, a Pentagon spokesman.

Warren said a Russian Su-24 aircraft, or Fencer, made 12 passes at low altitude near the USS Donald Cook, a destroyer that has been in the Black Sea since April 10. It appeared to be unarmed, he told reporters.

The incident lasted 90 minutes and took place on Saturday evening while the U.S. ship was conducting a patrol in international waters in the western Black Sea, Warren said. The ship is now in a Romanian port.

The Russian plane, accompanied by another Fencer that did not fly close to the U.S. ship, did not respond to multiple attempts by the Donald Cook to communicate with its pilot, he said.

Pentagon officials have not yet discussed the incident with the Russian government, Warren said.

Tensions have grown between Moscow and Washington in recent weeks over the situation in Ukraine, where pro-Russian separatists on Monday ignored an ultimatum to leave occupied government buildings and another group of rebels attacked a police headquarters.

Warren said the U.S. ship was not in danger during Saturday's incident.

"I would have difficulty believing that two Russian pilots on their own would choose to take such an action," Warren said.

"We've seen the Russians conduct themselves unprofessionally and in violation of international norms in Ukraine now for several months," he said. "These continued acts of provocations and unprofessionalism do nothing to de-escalate the situation in Ukraine."

(Reporting By Missy Ryan; Editing by Doina Chiacu)