The board also said another Oman entity, Oman Trading International, is willing to supply the entire feedstock requirement of the project, as well as to do the marketing for the resulting refined oil products, such as gasoline.
The main investor in the project - the Singaporean arm of India's Accord Group - has said as well it is fully confident the project will be implemented, according to the board.
Oman's oil ministry on Wednesday denied that it had agreed to make an investment in the refinery. That was only a day after the government in Colombo announced the Arab country's participation.
"No one on this side of the panel is aware of this investment in Sri Lanka," Salim al-Aufi, undersecretary of Oman's ministry of oil and gas, told a news conference.
"It came as news to me, I don't know who is signing the cheque for $3.8 billion," he said.
An industry source familiar with the discussions told Reuters on Wednesday that there had been talks concerning the project that involved Oman but that they were at an early stage.
Any big deal in Sri Lanka involving Indian investment will pose a challenge to China, which until recently had been on track to be the dominant foreign investor on the island.
India has become concerned in recent years about China muscling into Sri Lanka and other countries in a region where India is the traditional power.
China is the biggest buyer of Omani oil, importing about 80 percent of the Middle Eastern nation's overall crude exports in January, according to an Oman government website.