Ministers from the Organization of the Petroleum Exporting Countries are meeting Friday in Vienna for what could be a hard gathering.
Falih said the exact mechanics of any increase would be decided among all OPEC members on Friday.
Benchmark Brent crude LCOc1 was unchanged at $75.08 a barrel by 1037 GMT. Zanganeh cited recent demands for a production increase from U.S. President Donald Trump as a reason to oppose it.
By adding barrels to the market now, OPEC can stabilise or even increase inventories and ease shortages later in 2018/19.
Trump's involvement in pressing for OPEC to act - which in addition to his tweets include a behind-the-scenes request for a 1 million-barrel-a-day supply hike - could make it hard for Tehran to accept a compromise.
The preliminary accord allows for an additional 600,000 barrels a day of oil to flow onto the market, about 0.5 per cent of global supply, said a delegate.
Looming large over markets, however, were meetings scheduled on June 22-23 in Vienna of the Organization of the Petroleum Exporting Countries with other big producers, including Russian Federation.
Saudi Arabia said the move would translate into a nominal output rise of around 1 million barrels per day (bpd), or 1 percent of global supply.
The final production hike is expected to be less than the one million barrels as many producers may struggle to increase production.
Trump has in recent months repeatedly blamed OPEC for a spike in oil prices, but Zanganeh said it was U.S. sanctions on Iran and Venezuela that had fuelled fears of a supply crunch and put pressure on prices.
The energy ministers of Saudi Arabia and Iran also held last-minute talks ahead of the Opec meeting on Friday, the Financial Times cited Iran's Shana news agency as reporting.
Three OPEC sources said that if the proposal was approved, all OPEC members and their non-OPEC allies could raise supplies pro-rata, with Saudi Arabia adding about 0.25-0.3 million bpd.
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The output boost agreed on Friday had been largely priced into the market and was seen as modest.
Iran believes that OPEC is not a political body and so any politicizing of oil market and political use of oil against oil producers and consumers should be rejected, he highlighted. Countries with a lack of spare capacity, including Iran, Iraq and Venezuela, are resistant.
Since an increase of 1 million bpd would shrink the cut to about 1.8 million bpd from 2.8 million bpd, it could provide a compromise by keeping the existing deal while raising output. U.S. light crude was 80 cents higher at $66.34.
"How much oil do we need?. around 1 million (barrels per day, bpd) probably".
"There is going to be a sales lull that will keep these barrels trapped and the widening of the spread that we see will persist and get worse before it gets better", said John Kilduff, partner at Again Capital LLC in NY.
Analysts have called this week's OPEC talks the most fractious and politically charged in years.
Current restrictions were due to be in place until the end of 2018 but most commentators expect the meeting will result in some degree of production increase.
"As a group we can meet the 100 percent compliance".
OPEC is an worldwide organization with 14 members and doesn't take orders from anyone, Zanganeh said.
The convoluted plan shows the difficulty Saudi Arabia has in bridging the gap between the competing interests of different members.
"I think it's going to be a bad meeting", he told CNBC on the sidelines of a press conference with Barkindo.
The new deal would effectively roll back the deeper-than-intended cuts from nations such as Venezuela, returning the curbs back to the level originally agreed in 2016, the delegate said. The next formal OPEC meeting was set for December 3.
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