A virtual summit of Group of 20 energy ministers failed on Friday to devise a detailed plan to help resolve an unprecedented oil glut partly triggered by the coronavirus pandemic. Some producers continue to pin their hopes on President Trump, who has emerged in recent weeks as a top diplomatic presence in oil-market talks. The G-20 gathering came a day after an alliance of producers including the Saudi-led Organization of the Petroleum Exporting Countries failed to complete a collective oil truce with Russia and other oil-producing nations. The majority of countries at that meeting agreed to take part in oil-production cuts to support prices. Mexico refused to join production curbs and had yet to reach a deal with OPEC Friday, putting the broader international agreement in jeopardy.

OPEC had expected Friday’s G-20 meeting to show that the U.S., Canada, the U.K. and other producers not allied with the cartel can pull back 4 million barrels a day of output, according to delegates at Thursday’s meeting. OPEC and its allies including Russia are trying to complete a deal that would have them cut 10 million barrels a day. But the meeting ended with a press release that didn’t mention specific targets for oil-output reductions. “We recognize the commitment of some producers to stabilize energy markets,” said the press release. “We acknowledge the importance of international cooperation in ensuring the resilience of energy systems.”

Energy Secretary Dan Brouillette, who represented Mr. Trump at the G-20 meeting, told attendees Friday that U.S. production would fall by nearly 2 million barrels a day by the year’s end. And Norway and Brazil said they were either cutting production or planned to do so, according to people familiar with the deliberations. And the G-20 officials agreed to set up a special committee to monitor oil markets, according to the press release.

Mr. Brouillette has been the Trump administration’s point man in its efforts to help resolve a month-long oil-price war between Saudi Arabia and Russia. Behind the scenes, Mr. Trump has been making frequent late-night phone calls to Russian President Vladimir Putin, King Salman of Saudi Arabia and other key players in the oil market. The role of oil-world peacemaker is an unlikely one for Mr. Trump. Although he is leader of the world’s biggest oil-producing—and oil-consuming—nation, he has been a longstanding critic of cartel-based efforts to boost prices.

“We leave it to Trump to sort it out,” said a delegate who attended Thursday’s failed producers’ call. “He is the best OPEC negotiator today.” On Friday, Mexican President Andrés Manuel López Obrador said a phone call with Mr. Trump convinced him to cut output. Hours of talks with OPEC the previous day had failed to bring him on board.