Senate Democrats have also called for OPEC to increase production, as well as blaming Trump's policies and his decision to ditch the Iran nuclear agreement for high prices.
In earlier reports on the swap deal, an Iraqi oil official had said the initial flow of Kirkuk oil to Iran would be 30,000 bpd, but could rise to 60,000 bpd within a year-the initial duration of the deal-which the sides agreed could be extended.
Markets were disappointed with the modest output hike, sending crude prices soaring on Friday.
As one of the world's top producers, Russia's cooperation in the supply-cut deal is seen as crucial.
The move from the United States pinched India hard by sending pump prices to record highs and putting pressure on inflation, CAD (current account deficit) and government math by pushing up the oil import bill.
The increase was announced after ministers from the group met on Friday in Vienna.
The 24 nations in the supply-cut pact, known as Opec+, agreed in late 2016 to trim production by 1.8 million barrels a day but they have actually been keeping some 2.8 million barrels per day off the market.
"The aim of the deal is to return total compliance to the current output agreement to 100%". The minister said the difference between that amounts to "a little bit less than 1 million barrels".
But the joint communique did not spell out how the additional barrels would be divvied up, a key issue given Iran's insistence that cartel members should not be allowed to offset involuntary production losses in other member countries. Venezuela will raise its production when it can.
This week's OPEC talks in Vienna have been the most politically charged in years.
The production limits by the Organization of the Petroleum Exporting Countries and Russian Federation since 2016 have helped increase oil prices, with the benchmark US crude contract hitting its highest level in more than three years in May. "Hope OPEC will increase output substantially". "Need to keep prices down!"
OPEC is "at it again", to borrow Donald Trump's wording, but not in the way he imagined.
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