The priority at the moment was to ensure stability in the banking and financial system, he said.
Shadow chancellor George Osborne travelled from the Birmingham conference to London for a meeting about the crisis with Chancellor Alistair Darling and regulators at the Financial Services Authority.
Speaking afterwards, Mr Osborne described the meeting as "extremely positive".
"We will not write a blank cheque or fail to ask the right questions about proposed solutions," said the shadow chancellor.
"But we will do so in a spirit of co-operation because I think that's what the British people want to see at a time like this."
Liberal Democrat leader Nick Clegg said his party would also support measures to tackle the financial crisis, and "come together in the spirit of compromise in the interests of the British people".
He said the government should bring in an "unambiguous guarantee" to protect all British people's savings in British banks - at present only savings up to £35,000 are guaranteed.
The government has indicated it plans to increase the savings guarantee to £50,000 - and Mr Cameron called on new legislation to protect savings to be brought forward to next week when MPs return to Parliament.
Collapse of confidence
He said the Tories would give it their full support. He said they would also set aside concerns to allow the safe and rapid passage of a Bill to give the Bank of England powers to rescue failing banks.
BBC political editor Nick Robinson said Treasury sources believed the specific measures proposed were either unnecessary or would have no impact on the current crisis.
And Chancellor Alistair Darling later said he already had "the powers that I need and I've made it clear over Northern Rock, and this weekend with Bradford & Bingley, that I will do whatever is necessary".
During his statement to conference - a last minute change to the schedule - Mr Cameron said: "As if life wasn't already enough of a struggle with the cost of living going up people are worried this morning about their jobs, their mortgages, their savings, their pensions.
Cameron's address was memorable not so much for the actions he proposed but the tone he struck
"They get even more worried when they hear talk of a collapse of capitalism. People are confused and concerned. They want to know what's going on. They want to know what is going to happen next."
He added: "We have always been ready - at a time of national difficulty - to put aside party differences to help bring stability and help bring reassurance.
"Working across party lines is not just something we say because it might sound reasonable - it is something that may well be very necessary. There may well need to be a marshalling of public support behind some big decisions.
"This is a moment when democracies are being tested: we need to show that they can deal with crisis and difficulties like this one."
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