Ministers from the Organization of the Petroleum Exporting Countries are meeting Friday in Vienna for what could be a hard gathering.
Mr Zanganeh met with Khalid al-Falih, his Saudi counterpart, for private talks on Friday morning before the full Opec meeting.
Mustapha Guitouni, Algeria's energy minister.
Mohammed Barkindo, Opec secretary general.
Iran's Zanganeh has accused Trump of trying to politicise OPEC and said it was United States sanctions on Iran and Venezuela that had helped push up prices. "The already fragile world economic growth will be at threat if oil prices persist at these levels". They have since substantially overshot that target, with the reduction estimated at 2.8 million bpd.
Falih, in a nod to the problems with faltering production in Venezuela, Iran, and Libya, acknowledged that "not every country" will be able to join the production increase. Ministers at the event have also indicated that Iran, which was expected to oppose an increase might now agree to a production hike.
The Iranian publication Seda quoted anonymous sources as saying Zanganeh told the other producers that the proposed increase would pave the way for cuts in Iranian oil output that are likely to result from a reimposition of US sanctions against Iran in the fall.
Saudi Arabia and Russian Federation on Thursday used a pre-OPEC meeting in the Austrian capital to float a proposal of bringing an extra one million barrels each day to the market. Iran's output is also likely to fall in the second half of this year due to the new USA sanctions.
There's a good reason for the two countries' opposition - neither have the ability to increase their own production.
Iran is understood to want a coded critique of the USA, which recently ended an worldwide nuclear agreement with Iran, in the final Opec agreement on Friday.
Those additional supply losses have been largely unintentional, reflecting the collapse in Venezuela's oil industry and long-term declines in Mexican output.
OPEC has agreed to increase oil production by one million barrels a day after a stormy meeting that saw Iran walk out of negotiations.
The measure has helped re-balance the market in the past 18 months and lifted oil prices to around $73 per barrel from as low as $27 in 2016. That surge prompted the US president to complain on Twitter that the cartel was artificially inflating prices. Brent crude last month surged to a more than three-year high above $80 a barrel.
Trump's involvement makes it hard for Tehran to accept a compromise. Given this situation, there has been a lot of behind the scenes negotiations going on in an effort to reach some kind of compromise so OPEC and the other major producers can move forward with their plan to stabilize prices.
"If China's import demand dries up, more than 300,000 bpd of U.S. crude will have to find a new destination", energy consultancy FGE said, adding that "this will certainly depress U.S. Gulf Coast prices".
Saudi Arabia claims that production restraints and geopolitical factors have actually seen output fall by far more, to around 2.8 million bpd. Riyadh could also act unilaterally boosting output, as it did in 2011 after a meeting ended in acrimony without a deal.
OPEC and non-OPEC producers will meet on Saturday to iron out details of the pact and then again in September to review the deal.