Iran is among the nations with the highest oil serves, along with Saudi Arabia, which is the world's leading exporter of oil.
The letter calls on the president of OPEC to "remind" member states to "adhere to their commitments. and refrain from any unilateral measures undermining the unity and independence" of OPEC.
OPEC and non-OPEC countries said they would raise supply by returning to 100 percent compliance with previously agreed output cuts, after months of underproduction.
Late last week, Iran's Oil Minister Bijan Zangeneh urged the Organization of Petroleum Exporting Countries (OPEC) to prevent some of its members from increasing output without arriving at a consensus.
Saudi Arabia acknowledged the call took place, but mentioned no production targets.More news: Panos Panay fingers LG Display as screen supplier for the Surface Phone
In a statement issued Saturday night, the White House seemed to walk back Trump's tweet.
"Thanks to the work of President Vladimir Putin with the King and Crown Prince of Saudi Arabia, relations are in a unique phase, and this gives a great boost to the budget". Prices also have risen with ongoing unrest in Venezuela and fighting in Libya over control of that country's oil infrastructure.
"Iranian crude oil will be offered on the bourse and the private sector can export it in a transparent way", Jahangiri said at the event.
"We will surely do something to thwart the USA rallying cry that Iranian oil (exports) must be stemmed", First Vice President Eshagh Jahangiri said in statements broadcast on state television.
"The [Iranian] government has a plan. and God willing we are certain that we will be able to sell as much oil as we want".
Oil prices rose on Friday on worries that USA sanctions against Iran would take away significant volumes of crude oil from world markets while oil demand worldwide increases.
After the major oil producers got the desired price jump, they agreed this June to gradually raise output for fear of supply deficit on the market.