The minimum wage would rise to £8 an hour over the course of the next parliament if Labour wins the general election, the party has pledged.
Leader Ed Miliband said it was "not good enough" that one in five people in the UK were on low pay.
But the Conservatives said they had already delivered an above-inflation increase as, from October, the minimum wage will rise from £6.31 to £6.50.
The minimum wage for adult workers was £5.80 at the time of the last election.
Chancellor George Osborne suggested, in an interview with BBC Political Editor Nick Robinson in January, that the minimum wage would rise to £7 an hour in 2015 to return the level it was at before the economic downturn.
The rate is recommended by the Low Pay Commission, which is overseen by Liberal Democrat Business Secretary Vince Cable.
"By crashing the economy, Labour made everyone poorer and they haven't learnt their lesson”
Sajid Javid Conservative minister
Government sources have suggested that the rate would probably rise to £8 by the end of the next Parliament if it continued on current trends. The TUC has called for the minimum wage to increase to £10 an hour.
Mr Miliband announced the policy in interviews with the Sunday Mirror and Observer newspapers as Labour's annual conference got under way in Manchester.
The party says the £1.50 per hour increase would be worth £60 a week, or £3,000 a year, for the lowest paid.
"Too often people think that politics doesn't care about them," the Labour leader told the Sunday Mirror.
"They are the wealth creators just as much as the top entrepreneurs and the top business people. And we've got to reward them."
Tory cabinet minister Sajid Javid: "Ed Miliband would make people worse off."
He said the party would show "how we can become a country that rewards hard work once again".
In the Observer interview he added: "It is not good enough for us that one in five people in our country go out to work, make their contribution and are in low pay."
But Conservative Culture Secretary Sajid Javid said people would not take "lectures" from Labour on helping people on low pay.
"By crashing the economy, Labour made everyone poorer and they haven't learnt their lesson," he said.
"Ed Miliband would make people worse off with the same failed policies that got us into a mess in the first place - more wasteful spending, more borrowing and higher taxes."
The Liberal Democrats said the best way to help the low paid was to cut their taxes.
"Labour has refused to back tax cuts for working people," a spokesperson added.
Meanwhile, Mark Littlewood from free market think tank the Institute of Economic Affairs said the move would be "dangerous" for the economy.
The national minimum wage is the lowest hourly rate at which workers must legally be paid, although there are lower levels for workers aged 18-20, those under 18 and those working on an apprentice scheme.
It was introduced by Labour in 1997 and the level is reassessed annually by the Low Pay Commission, which then makes a recommendation to ministers.
October's above-inflation increase of 19p (3%) - announced in March - will be the first time in six years that the rise is higher than inflation.
The rate for 18 to 20-year-olds will go up by 10p to £5.13 an hour, a 2% increase.
The rate for those aged 16 and 17 will rise by 7p to £3.79, also a 2% rise.
Apprentices will earn an extra 5p an hour, taking their wages to at least £2.73.
In August the Consumer Price Index rate of inflation was 1.5%.
So we could see people taking home less because they will move into the income tax bracket or less because employers will reduce hours or even less still as they will be made redundant because some employers won't be able to afford the rise.