Chief Whip Andrew Mitchell was involved in an argument with an officer at the main entrance to Downing Street on Wednesday.
According to The Sun, he swore at the officer after he was stopped from leaving through the famous gates on his bike.
The paper reported a source who quoted Mr Mitchell as saying: "Open this gate, I'm the Chief Whip. I'm telling you - I'm the Chief Whip and I'm coming through these gates."
Officers had tried to get Mr Mitchell to leave through a pedestrian side gate but he refused, The Sun reported.
He is said to have relented only after being threatened with arrest under the Public Order Act.
Mr Mitchell is disputing the newspaper's version of events, but said in a statement last night that he "did not treat the police with the respect they deserve" on the evening in question.
He said: "On Wednesday night I attempted to leave Downing Street via the main gate, something I have been allowed to do many times before.
"I was told that I was not allowed to leave that way.
"While I do not accept that I used any of the words that have been reported, I accept I did not treat the police with the respect they deserve."
He said he had apologised to a supervising sergeant over the matter and would also apologise to the police officer involved.
A Downing Street source said Prime Minister had been made aware of the incident, welcomed Mr Mitchell's apology and was clear that police should be treated with respect at all times.
Mr Mitchell, a former shadow police minister, was given the key post of Chief Whip in a reshuffle two weeks ago, which sees him in charge of discipline in the Conservative Party. He previously served as International Development Secretary.
A Met Police spokesman said: "We have not made a formal complaint."