The statement comes amid fears of further plunges in the price of oil following the re-entry of Iranian oil into international markets after the lifting of Western sanctions on Sunday.
"Oman is ready to do anything that would stabilise the oil market," Rumhy said, "5 or 10 percent is what I think we need to cut and everyone has to do the same."
Rumhy urged all other oil producing countries to also work on stabilising the oil market.
Brent crude fell to less than $28 a barrel on Monday, losing a fifth of its value so far this year, as fears that the lifting of Western sanctions on Iran will add to the existing oversupply of oil by at least half a million more barrels a day.
Oman's statement follows calls by outgoing OPEC President Emmaneul Kachikwu for an emergency meeting of OPEC member states to discuss potential production cuts.
OPEC is deeply divided with some member nations willing to cut production to raise prices but others, notably OPEC's most powerful member Saudi Arabia, refusing further cuts in order to increase market share against non-OPEC producers.
Oman currently produces nearly one million barrels of oil per day, a number which is not expected to rise this year, according to the oil minister.
The rapid fall in the price in oil from 2014 onwards is attributed to a major over-supply of oil both by OPEC producing nations and increased supply of US shale oil, causing a glut on markets compounded by a slowing of the Chinese economy.
Budgets across Middle-Eastern oil producing nations have been significantly affected by cuts.
Saudi Arabia recently announced a cut in state petrol subsidies to make up the budget shortfall in a move echoed by neighbouring nations.