Chancellor George Osborne has warned that "self-defeating" increases to the minimum wage could "cost jobs".
Cabinet ministers including Business Secretary Vince Cable and Work and Pensions Secretary Iain Duncan Smith are reportedly pressing for an above-inflation rise of 50p or more.
Mr Osborne said he too wanted to see the £6.31 hourly minimum wage rise.
But he said it should be left to the Low Pay Commission to set the appropriate level.
His comments came during a visit to Enfield, north London, to highlight the forthcoming introduction of the new Employment Allowance, which will allow every business and charity to claim the first £2,000 a year back off their National Insurance bill.
The chancellor said the move, announced in the 2013 Budget and due to take effect on 6 April, would mean companies could "hire more people, invest more, do all the things we need to see as part of our long-term plan for Britain to increase jobs and bring economic prosperity to this country".
But Mr Osborne downplayed the prospect of the government over-ruling the Low Pay Commission if it fails to call for a "significant" rise to the minimum wage when it reports next month.
Mr Osborne said: "I think everyone wants to see an increase in the minimum wage. I would like to see an increase in the minimum wage.
"But it has to be done in a way that doesn't cost jobs, because that would be self-defeating.
"We have a Low Pay Commission as a body that exists to make exactly that judgment.
"What we have got to do as a country is get the balance right between supporting business, growing our economy and making sure it is a recovery for all, and that is what our long-term plan is all about delivering."
Mr Cable said he would only back a substantial rise in the minimum wage if it did not damage jobs.
"This is why I asked the independent Low Pay Commission what economic conditions would be needed to allow for significant rises in the minimum wage without damage to employment," he said.
"The minimum wage strikes a key balance between protecting the low paid and making sure they can find work," he added
"But as the economy starts to recover, the benefits of growth must be shared fairly and equally by everyone."
Downing Street rejected the suggestion of any cabinet split over the minimum wage, saying that the government was not going to pre-judge the outcome of the Low Pay Commission's review of the minimum wage.