BRUSSELS — NATO and Russia remain at loggerheads over Ukraine, the alliance’s top official said Monday, after their ambassadors met in a fresh attempt to improve their acrimonious relations.

NATO Secretary General Jens Stoltenberg said that the 28-nation military alliance and Russia “have profound disagreements on the crisis” in Ukraine.

He said NATO allies “reiterated their strong support for Ukraine’s sovereignty and territorial integrity,” and insisted that they would never “recognize Russia’s illegal and illegitimate annexation of Crimea.”

Stoltenberg’s remarks came after the NATO-Russia Council, their main forum for dialogue, met in Brussels Monday for more than three hours. There was no immediate comment from the Russian side.

It was the third time this year that diplomats have tried to resolve some of their differences.

The meeting also included talks on ways to avoid incidents and accidents between Russian and NATO forces.

Russia has annoyed NATO with snap war games or by buzzing the alliance’s ships and aircraft with fighter jets, as well as what NATO sees as aggressive use of propaganda.

Douglas Lute, the U.S. ambassador to NATO, told ABC news on Sunday that “I don’t believe that anyone in Russia today intends to attack NATO.”