The allegations centre on a claim made by Kuwaiti MP Ahmad al-Saadun this week that a letter was sent in April by Jordan's Prime Minister Faisal al-Fayez asking Kuwait to deposit revenues from the emirate's oil grant into a US account.
The account belongs to private firm Free Market Petroleum Ltd. registered in the US and chaired by a Turkish national.
Saadun released copies of what he said were the letter and a decision taken at a Kuwaiti cabinet meeting on 18 April approving the request and ordering Kuwait Petroleum Corp to transfer the money into the company's account.
Jordan has moved fast to counter the allegations.
"All revenues coming from the sale of oil (in the form of a Kuwaiti grant) which cannot be refined in Jordan are transferred to the Jordanian central bank," Finance Minister Muhammad Abu Hammur said on Wednesday.
He said that Jordan's government "normally brings in an oil company to sell on the international market the (Kuwaiti) petrol as it cannot be refined in Jordan".
The revenues are transferred to the central bank which buys the quality of crude which Jordan's refinery can handle, the minister said.
"Jordanians don't understand why the prime minister asked for the transfer of revenues from the sales to a private account in the United States"
Unnamed former minister,
The letter released by Saadun authorises a transfer of funds to the company but "not a green light for the firm to sell the oil", said a former Jordanian minister, asking not to be named.
He said the government still owed the Jordanian people a clarification.
"Jordanians don't understand why the prime minister asked for the transfer of revenues from the sales to a private account in the United States," the minister added.
Jordan depended on Iraq for all its oil needs before last year's US-led invasion of its eastern neighbour, importing 5.5 million tonnes annually by road, half of it for free, and the other half at a preferential price.
As supplies were cut off with the outbreak of the war, Jordan struck a deal with the oil-producing giants in Saudi Arabia, Kuwait and the United Arab Emirates to receive 100,000 barrels of crude oil per day.