Qatar would continue to produce oil and seek deals in countries including Latin America's top oil producer Brazil, said Kaabi.
Qatar produces about 650,000 barrels of oil per day, less than 2 per cent of total output, making it a minnow in Opec.
Saudi Arabia, the United States and Russian Federation are the biggest producers in OPEC "so is it really worth it to someone like Qatar to go to Vienna to meet with someone who will lead the meeting and who is your enemy?" said Thierry Bros, a researcher with the Oxford Institute for Energy Studies.
Twitter handles were abuzz with the news break."It is better if OPEC breaks, free market may stablise oil prices", read a tweet.
The cartel's largest member, Saudi Arabia, along with three other countries, has cut trade and transport ties with Qatar for the past 18 months, accusing Qatar of supporting terrorism and the Saudis' largest regional rival, Iran.
It announced the decision at a press conference Monday, just days ahead of a crucial meeting on Thursday.
The minister said that Qatar has been in OPEC for 57 years, but that the country's impact on OPEC production decisions was small.
OPEC is responsible for one-third of the world's oil output and members have to abide by strict production quotas.
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With daily oil production of around 600,000 to 700,000 barrels and a larger natural liquefied gas profile, Qatar has made a decision to exit the Organisation of Petroleum Exporting Countries (OPEC) in 2019, to leverage on growing its LNG portfolio. But the move also draws another line of division with Saudi Arabia, the only country with which Qatar shares a land border.
"Basically, Qataris have brought the biggest weapon out and it only means more instability between the Qatari and Saudi relationship", Naeem Aslam, chief market analyst at ThinkMarkets, told The National.
Qatar's first $15 million in cash, delivered in several suitcases, came as Egyptian mediators negotiated a "long-term" ceasefire between Hamas and Israel.
Qatar has been locked in a diplomatic dispute with Opec's de facto leader Saudi Arabia for several months.
International Brent crude oil futures were up $2.89 per barrel, or 4.9 per cent, at $62.35 a barrel.
Saudi Arabia, the UAE, Egypt and Bahrain started boycotting Qatar a year ago, accusing Doha of funding militants across the Middle East and fostering ties with Iran, charges that Qatar denies.
Among its members, Saudi Arabia is by far its largest oil exporter, hitting a record high in November of over 11 million barrels of oil a day.
The state petroleum agency that reported the news said that the body had been informed of the move.