President Donald Trump issued a new demand for the world's leading oil producing countries to stabilize oil markets with more supply, only days after the United States and Saudi Arabia discussed the possibility of the kingdom releasing more of its own crude to dampen surging prices.

On Twitter, Trump called on OPEC countries, fresh from a meeting in which they decided to raise oil output by an indeterminate amount, to do more to bring down crude prices. Trump indirectly linked U.S. foreign policy to his demand, saying the U.S. defends some oil producing countries "for very little" money.

Trump tweet

The president's call to "reduce pricing" was an apparent reference for oil producers to churn out more supply in order to contain spiking oil prices. On Tuesday, crude closed near $78 per barrel, driven higher by a sharp drop in U.S. inventories and the expectation of more drivers hitting the road for the July 4 holiday.

Barely a week after OPEC's , Trump surprised the world on Saturday by announcing a new side agreement with the Saudis to compensate for supply shortages from two crisis-hit producers, Iran and Venezuela. Both countries resisted the oil cartel's decision last month, even though OPEC demurred on how much it would boost supply.

The members of OPEC include countries such as Qatar, Saudi Arabia and Kuwait, Persian Gulf states that have long enjoyed strong diplomatic and military ties with the United States. Trump's "two way street" remark appeared to be a veiled suggestion that the U.S. could temper support for these countries, if they didn't do more to alleviate upward pressure on the market forces driving up prices.

The president and King Salman agreed that Saudi Arabia, at its discretion, would add more output to a market that’s seen crude shoot to its highest level in more than 3 years above $74 per barrel. The Saudis, however, did not confirm any specific production targets — the idea of which came under sharp criticism from some market observers.

“This incident with the Saudis and the U.S. administration is just noise … You cannot order 2 million barrels like ordering a coffee somewhere,” Beat Wittmann, a partner at financial consultancy Porta Advisors, told CNBC’s “Squawk Box Europe” on Monday.

With gasoline prices climbing above $3 per gallon in many parts of the United States, Trump has come under increasing pressure. Economists say higher gas prices act as a de facto tax hike — which is ironic given that the centerpiece of Trump's tenure thus far has been a broad-based tax cut.

--CNBC's Sam Meredith contributed to this article.