EDF Energy has said its average gas and electricity price will rise by 3.9%.
The company, one of the UK's big six energy suppliers, is the latest provider to raise bills, but it says its rise is "half" that of its rivals.
The company says its new average standard variable price from 3 January will be £1,300, a rise of £49 a year.
Energy Secretary Ed Davey told the BBC he welcomed the fact that one of the big six suppliers had produced a price rise closer to inflation.
"Now people will see they have [a] choice. It isn't just the smaller suppliers offering lower prices," he added.
He also warned that energy firms needed to "respond to customers' concerns" if they wanted to avoid damaging their reputation.
Mr Davey's warning came on the day energy bosses sought to defend their industry in a bid to end political criticism of their companies.
At the annual conference of industry body Energy UK, Mr Davey said that power firms should not treat the public as a "cash cow".
In response, Energy UK said the industry was "already working hard to ensure everyone can keep the lights on and stay warm this winter".
"The best way to do this is for everyone to work together, which is why this tit-for-tat Punch and Judy show of insults is so unproductive," a spokesman said.
EDF said it was not passing on the rising cost of the government's green levies, which it estimates would have added another £50 to the average annual household bill.
Its move follows Prime Minister David Cameron's pledge to "roll back" green energy levies.
The government is currently reviewing its environmental policies to see if they can be delivered more cost-effectively.
If the government makes bigger changes to the costs of its social and environmental schemes than EDF expects, it said it would pass these savings on to customers.
However, EDF warned that if the government failed to reduce green levies, the firm might have to put up its prices further.
"If changes to social and environmental programmes are less than anticipated, the company may have to review its standard variable prices again," it said in a statement.
In response, shadow energy secretary Caroline Flint reiterated Labour's plans for a freeze in energy prices if the party wins the next election.
She said: "This latest price hike shows that nothing less than a price freeze will do, because, as EDF has made clear, even if the government does make changes to green levies, the energy companies are still planning to put up people's bills anyway."
EDF chief executive Vincent de Rivaz said the industry had to "challenge the cost and affordability" of government green schemes.
"Something can and must be done for consumers," he added.
EDF, which has 3.7 million residential customers, is the latest energy provider to increase its prices.
SSE said it would increase prices by 8.2% from 15 November, British Gas's prices are due to rise by 9.2% on 23 November, Npower said its dual-fuel bills will go up by 10.4% on 1 December and Scottish Power's price rise will be 8.6% for dual-fuel energy bills from 6 December.