The prime minister said the Government wanted to keep business taxes low, but in return businesses must accept that they have to pay their fair share.
But he made clear he was not convinced by the case for new laws to force companies to pay their taxes, telling an audience at Unilever's headquarters in Mumbai that it would be "difficult" to do.
Cameron has made transparency over tax a key priority of Britain's presidency of the G8 group of world economic powers this year, in the wake of a series of controversies over the arrangements of companies like Starbucks, Amazon and Google, which were shown to be paying little tax in the UK.
He said today: "I believe in low taxes. Governments should be trying to get their rates of tax down so they are competitive, but then I think it is only fair to ask businesses to pay them.
"My position is taxation is a part of the cost of doing business, but I think there is a deal.
"The deal in my country, which I want to be very frank about, is that you have a government that is cutting the levels of business taxation, we are cutting the rate of corporation tax on company profits, down to 21%. That is a good, low, competitive rate.
"The message to business should be, 'If we are cutting this rate of tax down to a good low level, you should be paying that rate of tax, rather than seeking ever more aggressive ways to avoid it'.
"I think there has been a problem in this debate in the past, in that people have said there is a difference between tax evasion - which is illegal and should be pursued by the full force of the law - and tax avoidance, which is perfectly legal and OK.
"I think the problem with that is that there are some forms of tax avoidance that have become so aggressive that there are moral questions that we have to answer about whether we want to encourage or allow that sort of behaviour."
He added: "Some would say, 'Just change the law to make aggressive avoidance illegal', but, with respect to my friends in the accountancy profession, it is difficult to do that.
"I think there is a legitimate debate to say very aggressive forms of avoidance are not appropriate.
"And particularly, in a country which has set a very low tax rate, it is fair to ask people to pay it."
Responding to Cameron's comments, Oxfam head of policy Max Lawson said: "We welcome the prime minister's promise to clamp down on tax avoidance that costs both the UK and developing countries tens of billions of pounds a year.
"The challenge for the prime minister will be to turn his tough rhetoric into reality - he could start by clamping down on secrecy in the tax havens over which the UK has control."