Falih said that, during a visit to Bandar Seri Begawan, he conveyed to Brunei's energy minister the kingdom's keen interest in fostering cooperation with Brunei on all levels.
While US shale output growth and the shutdown of refineries for maintenance have slowed the impact of cuts by Opec and its partners, the Saudi minister said he's confident the global oil market will soon rebalance and return to a "healthy state".
"It looks much more likely that OPEC are going to continue the deal over the rest of the year, which should be supportive of prices", said Tom Pugh, commodities analyst at consultancy Capital Economics.
Markets however have been impacted by a combination of slow seasonal demand and refinery maintenance, some growth in non-OPEC supply - especially in the USA - and the action of financial players in the market, he said, adding that all of this has slowed down the impact of the production cuts agreed by the coalition of producers in December.
Russian Federation and Saudi Arabia, the largest of the 24 nations that agreed to cut production, are reaffirming their commitment to the deal amid growing doubts about its effectiveness.
With hedge funds embarking on a fresh cycle of short selling in oil, OPEC ministers seem to have concluded it was no longer practical to wait another two weeks until their formal meeting on May 25.
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In their view, production cuts would need to be extended into the middle of 2018, a concern Falih acknowledged implicitly.
"He also expected global oil demand to grow at a rate close to a year ago". However, under current OPEC and Non-OPEC production accord, a great deal of understanding and awareness led to record high production discipline amongst all conventional oil producers.
"The producer coalition is determined to do whatever it takes to achieve our target of bringing stock levels back to the five-year average", Al-Falih was reported as saying.
In the past, oil prices have risen significantly in the aftermath of an announcement by OPEC that it is cutting production, according to researchers, who examined all OPEC announcements between 1983 and 2008.
Brent crude was up 40 cents at $49.50 a barrel by 0930 GMT. "OPEC members have no choice but to talk up prices by signalling an extension to the production cuts agreement".