The expenses relate to Nadhim Zahawi's second home in the village of Tysoe, near Banbury, in his constituency of Stratford on Avon in Warwickshire.
The MP said he had contacted the expenses watchdog.
The Sunday Mirror reported last week that Mr Zahawi had claimed some Â£6,000 in the year up to March.
Mr Zahawi said the watchdog, the Independent Parliamentary Standards Authority, had included claims for the previous year and the figure was nearer Â£4,000.
In a statement issued on Saturday, he said: "I have been looking into this matter further and can confirm that all claims for heating fuel relate purely to my second home.
"However, I have made a mistake with my electricity claims.
"On investigation I have discovered that electricity for a mobile home located in the stable yard, and electricity for the stables themselves, was linked to my house.
"Whilst a meter was installed in the stable yard, I have only been receiving one bill; it was wrong to assume I was receiving two and to have not checked this sooner.
"I am mortified by this mistake and apologise unreservedly for it. I will obviously be paying back any money that was wrongly claimed immediately."
Jeff Kenner, Labour councillor for nearby Shipston-on-Stour, said the news was "outrageous", with many local people "struggling with their fuel bills".
He called for a full investigation into the matter, but said Mr Zahawi's position was looking "untenable".
Earlier this month, Deputy Prime Minister Nick Clegg defended MPs claiming back the cost of energy bills on their second homes.
Mr Clegg said expenses were there to help MPs with the cost of living and working in two different places.
Mr Kenner said: "People can understand that it's important for an MP to have a home in the constituency, but it just needs to be something modest, something he can visit constituents from.
"On his website he says he wants to restore trust in politicians and clean up politics.
"But not only has he claimed for his second home, but he has claimed for the stables, which is part of the stable yard business."
A Conservative MP has apologised for claiming parliamentary expenses for electricity to supply his stables and a mobile home in the stable yard.