SIMI VALLEY, Calif.—Senior U.S. military leaders have proposed sending more forces into Europe on a rotating basis to build up the American presence and are stepping up training exercises to counter potential Russian interference with troop transfers in the event of a crisis with Moscow.

The new steps would allow for the presence of multiple U.S. brigades in Europe at any given time, increasing that number above current limits.

They were outlined at a forum here over the weekend by military and defense leaders, who condemned military aggression and threats from Russian President Vladimir Putin and warned that the U.S. must not let Moscow’s cooperation with the West in Syria distract from the conflict in Ukraine.

Russia has been involved in diplomatic talks over the war in Syria and the future of the regime of its ally President Bashar al-Assad. In late September, it launched a campaign of airstrikes in support of Mr. Assad’s government.

Gen. Philip Breedlove, the supreme allied commander of the North Atlantic Treaty Organization, said he would like to see more brigades committed to Europe as rotational forces. Decisions on the proposal, he said, will be made “in the next couple of months.”