That would rise to six months for a second violation and three years for a third, aides said.
The announcement came as Work and Pensions Secretary Iain Duncan Smith prepared to give details of the universal credit, a single welfare payment which officials say will simplify the current complex benefits system and make two and a half million people better off.
Cameron's coalition government, which took power in May, describes the plans as the most radical since Britain's wide-ranging welfare state was put in place just after World War II.
Welfare now accounts for roughly a third of government spending.
Explaining the plans for a "claimant contract", Cameron said: "It simply has to pay to work. You can't have a situation where if someone gets out of bed and goes and does a hard day's work they end up worse off.
"That's not fair. And it sends entirely the wrong message, both to those on benefits and to the hard-working majority who are being asked to support them," said Cameron, who is in South Korea for a G20 summit in Seoul.
Some have criticised the government's proposals on welfare, which ministers hope will be approved by parliament and made law next year.
Earlier this week, the leader of the world's Anglicans, Archbishop of Canterbury Rowan Williams, said he had a "lot of worries" about proposals to make long-term claimants of unemployment benefit carry out month-long placements of 30 hours a week doing unpaid tasks like clearing litter.
"People who are struggling to find work and struggling to find a secure future are I think driven further into a sort of downward spiral of uncertainty, even despair when the pressure's on in that way," he told the BBC.
Aides stressed that the "claimant contract" scheme was not "100 percent inflexible" and that some people could be exempt if they had an "incredibly good excuse".
Under the existing system, claimants who do not cooperate with officials can lose their unemployment benefit for 26 weeks maximum but aides insisted that this rarely happened.
Around 1.5 million people in Britain currently claim unemployment benefit, formally known as jobseekers' allowance.
Welfare was one of the areas hit hard by the deepest public spending cuts in decades which Cameron's Conservative-Liberal Democrat coalition government announced last month.
It is battling to reduce a record deficit of 154.7 billion pounds inherited from the previous administration under Labour's Gordon Brown and Tony Blair.