Writing Thursday on Twitter, Mr. Trump said he had spoken that morning to Prince Mohammed, who told him he had been in touch with Mr. Putin, adding: “I expect & hope that they will be cutting back approximately 10 Million Barrels, and maybe substantially more which, if it happens, will be GREAT for the oil & gas industry!” In a subsequent tweet, Mr. Trump said the production cut could be five million barrels per day larger.

American oil executives immediately reacted positively to the tweet. “I’m totally surprised and I’m glad the president took charge,” said Scott Sheffield, the chief executive of Pioneer Natural Resources, a major Texas oil company, who has urged the Trump administration to put pressure on Saudi Arabia and Russia.

But the Kremlin quickly played down Mr. Trump’s statement. Dmitri S. Peskov, a spokesman for Mr. Putin, told the Interfax news agency that the Russian president had not spoken with the Saudi crown prince. “No, there was no conversation,” he said.

Tass, a Russian state news agency, carried a more pointed exchange in which the Kremlin spokesman declined to say whether Mr. Trump might be manipulating markets. Asked if Mr. Trump had “intentionally mistaken” news about a phone call, Mr. Peskov said, “It’s difficult for me to answer.”

Oil prices have been hammered in recent weeks as the coronavirus pandemic has all but eliminated travel and dampened demand for energy. The price war that broke out between Saudi Arabia and Russia last month intensified the decline.

After failing to reach a deal on production cuts in March, Saudi Arabia and Russia began pumping huge amounts of oil, adding to a world glut. One aim has been to gain market share from American producers that have been increasing output and exports in recent years. But as Saudi Arabia has been shipping new production, it has been having trouble finding buyers.

The combination of slumping demand and the contest between two of the world’s largest oil producers had pushed crude oil prices down by 55 percent in March alone, wreaking havoc on the energy industry, with oil companies slashing budgets and refineries cutting production of gasoline, diesel and jet fuel.