The world’s two biggest crude-oil producers, Russia and Saudi Arabia, sent petroleum prices higher Monday with a joint statement that output cuts should be extended into March 2018.

The rare joint statement is the strongest signal yet that the Organization of the Petroleum Exporting Countries and a coalition of producers outside the cartel will continue their efforts to influence oil prices by cutting supply. OPEC’s 13 members and 11 non-OPEC producers agreed last year to cut almost 1.8 million barrels a day through June in...