Donald Trump said on Saturday he had received assurances from King Salman of Saudi Arabia that the kingdom would increase oil production “maybe up to 2,000,000 barrels”, in response to turmoil in Iran and Venezuela.

Saudi Arabia acknowledged the call took place, but mentioned no production targets.

Trump wrote on Twitter that he had asked the king in a phone call to increase oil production “to make up the difference … Prices to [sic] high! He has agreed!” A little over an hour later, the state-run Saudi Press Agency acknowledged the call, but offered few details.

“During the call, the two leaders stressed the need to make efforts to maintain the stability of oil markets and the growth of the global economy,” the statement said.

It added that there also was an understanding that oil-producing countries would need “to compensate for any potential shortage of supplies”. It did not elaborate.

Oil prices have edged higher as the Trump administration has pushed US allies to end all purchases of oil from Iran. Prices have also risen given ongoing unrest in Venezuela, as well as with fighting in Libya over control of that country’s oil infrastructure.

Last week, members of the Organization of the Petroleum Exporting Countries (Opec) cartel led by Saudi Arabia agreed to pump 1m barrels more crude oil per day, a move that should help contain the recent rise in global energy prices.

However, summer months in the US usually lead to increased demand for oil, which would push up the price of gasoline in a midterm election year. A gallon of regular gasoline sold on average in the US for $2.85, up from $2.23 a gallon last year.

Trump’s comments came as global financial markets were closed. Brent crude stood at $79.42 a barrel.

Saudi Arabia currently produces about 10m barrels of crude oil a day. Its all-time record is 10.72m barrels a day. Trump’s tweet offered no timeframe for the additional 2m barrels – whether that meant per day or per month.

The Trump administration has been counting on Saudi Arabia and other Opec members to supply enough oil to offset the lost Iranian exports and prevent oil prices from rising sharply.

The administration has threatened close allies such as South Korea with sanctions if they do not cut off Iranian imports by early November. South Korea accounted for 14% of Iran’s oil exports last year, according to the US energy department. China is the largest importer of Iranian oil with 24%, followed by India with 18%. Turkey stood at 9% and Italy at 7%.

The state department has said it expects the “vast majority” of countries will comply with the US request.

Trump announced in May that he would pull the US out of a 2015 agreement over Iran’s nuclear program, and would re-impose sanctions on Tehran. Previously, the administration said only that other countries should make a “significant reduction” in imports of Iranian crude to avoid US sanctions.