MOSCOW—Russia has withdrawn key defense advisers from Venezuela, an embarrassment for President Nicolás Maduro as Moscow weighs the leader’s political and economic resilience against growing U.S. pressure.

Russian state defense contractor Rostec, which has trained Venezuelan troops and advised on securing arms contracts, has cut its staff in Venezuela to just a few dozen from about 1,000 at the height of cooperation between Moscow and Caracas several years ago, said a person close to the Russian defense ministry.

The...