State-run Saudi Aramco plans to raise capacity to 13 million bpd from 12 million bpd, Chief Executive Amin Nasser said, adding that the move was ordered by the Energy Ministry.
"The company is exerting its maximum efforts to implement this directive as soon as possible," Nasser said.
No timeframe was given for the plans, which will require billions of dollars of investment.
The virus has prompted lockdowns in major economies such as China and Italy, disrupting businesses and sending shares into tailspin.
Moscow also said supporting prices simply helped boost costlier production in the United States, whose output has surged above that of Saudi Arabia and Russia. U.S. producers, by law, are barred from participating in any supply pacts.
The U.S. government slashed its forecast for U.S. oil output in 2020, saying it would rise by 760,000 bpd not the 960,000 bpd it previously forecast, and would drop by 330,000 bpd in 2021 to 12.66 million bpd.
Even as the Abu Dhabi and Riyadh promised more supplies, OPEC slashed its forecast for global oil demand growth this year and said further reductions might follow.
Brent was trading 4% down below $36 on Wednesday, off this week's low of about $31 but 45% lower than at the start of year.
Saudi Arabia's influence on oil markets is much akin to a central bank's role in financial markets. The kingdom holds nearly all the world's spare capacity and can turn the taps on and off to deal with supply shortfalls or surpluses.
But the kingdom has increasingly voiced frustration about acting as the world's main "swing producer", propping up prices by much bigger cuts than others, while its reserves are among the world's biggest and its oil among the cheapest to extract.
The clash between Saudi Arabia and Russia has triggered panic selling of shares on Wall Street and other stock markets that were already pummelled by the virus outbreak.
U.S. oil firms have rushed to cut dividends and spending.
Oil companies in Canada's energy-rich Alberta are expected to announce layoffs and export cuts soon after oil prices plummeted, the Canadian province's premier said on Wednesday.
Saudi Arabia last embarked on a $100 billion push to raise its capacity more than a decade ago amid a price boom fuelled by China's growth. Since then, Saudi officials have brushed aside questions of new investment to boost capacity.
