KIEV, Ukraine — Gay rights groups in Ukraine celebrated a milestone on Sunday — holding a parade without being chased or attacked by right-wing opponents. But the march, in Kiev, was guarded by police and security forces who sealed off much of the city center and warned participants not to linger afterward.

About 2,000 people turned out for the parade, called KyivPride. No violence was reported at the event, but a participant was beaten in the downtown area an hour or so afterward, organizers and the police said.

The outcome was a striking contrast to last year, when members of far-right organizations attacked the 300 or so marchers, injuring dozens. Similar violence appeared likely to unfold on Sunday after right-wing paramilitaries, emboldened by their popularity for fighting in the war against Russian-backed separatists in the east, vowed to shut down the march.

“In short, it will be a bloody mess on June 12 in Kiev,” Artem Skoropadsky, the spokesman for one group, the Right Sector, wrote in a joint statement with another group, the Organization of Ukrainian Nationalists.