Operating from the Romanian Mihail Kogalniceanu Air Base near Constanta on the Black Sea coast, the two Typhoon jets responded to the suspected bomber aircraft heading west toward NATO airspace, the RAF said in a statement.
It said the Russian aircraft did not enter NATO airspace and that the Typhoons patrolled the skies for a short period as a deterrent before returning to base.
Earlier in July, Russia's defense minister accused NATO of having bases "snuggled" up to its borders.
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"I have long wanted to give American colleagues a globe so they can look at it and explain why the declared 'enemies of America,' are located in the Middle East and the Far East and all their military bases and forces are snuggled up to Russian borders," Russian Defense Minister Sergei Shoigu said in a newspaper interview published as NATO began a two-day summit.
Shoigu appeared to be referring to the U.S. missile defense shield, which Washington says is intended to protect against attacks by Iran. Elements of that system are located in eastern Europe, near Russia's western borders.