Mr Cameron was speaking a day ahead of the Autumn Statement, in which he said Chancellor George Osborne will set out "the next steps in a long-term plan to turn our country round".
The Prime Minister insisted that Britain must stick to the coalition Government's austerity plan to get rid of the deficit by 2018, and said that once that point has been reached he wants to go further and start paying off the debt accumulated over many years.
Mr Osborne set out the ambition to run a surplus after 2018 - by spending less than the Government takes in from tax and other revenues - in his speech to the Conservative annual conference, sparking suggestions that austerity would continue until 2020 at least under the Tories.
But Mr Cameron said today that paying down debts did not necessarily mean forswearing tax cuts.
"The two aren't alternatives," he told the BBC. "It is possible to reduce people's taxes as your economy recovers.
"Of course, we are going to be looking ahead to a time when, yes, if the economy continues to grow and, as it were, the sun continues to shine, we should be fixing the roof when the sun is shining, as the last government failed to do.
"That means not just getting rid of our debts in good years but trying to put some money aside.
That is what Britain should be trying to do."
Asked if he wanted the mini-budget to give voters a clear view of what the public finances would be like over the next five years if he remained in Downing Street, Mr Cameron said: "I do want to do that and I will do that and the Chancellor will do that in this Autumn Statement by saying we have a long-term plan.
"It has involved difficult decisions about spending, about getting our deficit down. But this long-term plan is paying off. We are on the right track, we should stick to that track, recovering our economy, getting jobs for our people and over time really fixing for the long term the mess we were left in the public finances.
"Be very clear, this Autumn Statement is about the next steps in a long-term plan to turn our country round."
Earlier, industry groups welcomed an expected freeze in business rates set to be announced by the Government, but said they still believe the system needs to be reformed.
Mr Osborne is expected to confirm tomorrow that rate rises will be limited to 2% instead of being linked to inflation, after strong lobbying from a number of organisations.
Business rates were set to rise by 3.2% next year, based on September's retail prices inflation rate.
John Longworth, director general of the British Chambers of Commerce, said: "It is heartening that the Chancellor appears to be listening to business, and is planning to limit the damage caused by relentless business rates increases.
"But a tax rise is still a tax rise. Although a cap on rates would spare businesses some £300 million in tax hikes, and reliefs help many of the smallest firms, companies of all sizes will still be paying hundreds of millions more in rates to the Exchequer next year than the £27 billion they are expected to pay in this year.
"The business rates system is still iniquitous, still broken, and still in need of fundamental reform.
"Businesses in Britain still pay far more in property taxes than their counterparts in countries like Germany and France - which undercuts the Government's stated aim of maximum tax competitiveness. A cap on rate rises is better than nothing, but not nearly good enough."
Steve Radley, director of policy at EEF, the manufacturers' organisation, said: "Action on business rates, which are a fixed cost regardless of trading conditions, will help ease the pressure on margins.
"But for industry, the top priority must be addressing energy costs that are racing ahead of its competitors abroad."
Mr Cameron has signalled he is planning further action to reward marriage through the tax system, on the eve of the expected introduction of an allowance for some married couples.
Mr Osborne is expected to use his Autumn Statement to announce details of a transferable tax allowance worth £200 a year to an estimated four million couples from 2015, at a cost of £700 million.
But the Prime Minister - who made recognising marriage in the tax system a central plank of his general election manifesto in 2010 - told reporters that he regards it only as "the start of something" and he wants to go further when he is able to.