The NHS's Cancer Plan has seen an increase in survival rates
Patients in England suspected of suffering from cancer will have the right to see a specialist within two weeks, ministers are due to announce.
Primary care trusts would be required to pay for private consultations if NHS hospitals cannot meet the timescale.
The pledge will be part of the government's draft legislative programme to be unveiled on Monday.
Cabinet minister Yvette Cooper said it would focus on job creation and giving people more say over public services.
BBC News political correspondent Iain Watson says the government is keen to show people can still expect good service from the NHS despite an expected squeeze on public spending.
Prime Minister Gordon Brown is set to launch a major policy document, called Building Britain's Future, alongside the draft legislative programme as he seeks to lay out his vision in the run-up to the next election.
Ms Cooper, the work and pensions secretary, said the document would focus on building a fairer society, tackling youth unemployment and preparing the country for a return to economic growth.
On public services, it will outline plans to reduce Whitehall targets and extend new rights - such as the two-week cancer pledge - to the users of public services.
Ms Cooper defended the scrapping of performance targets - a cornerstone of Labour policy since 1997 - saying they had made a "big difference" to improving services at a time of huge investment but people now expected different things.
"Having made those improvements, the next step we now need is to be able to say, 'okay, those services are now accountable to local people'," she told the BBC's Politics Show.
"Local people should be entitled to things from their health service, from their education service, and that's how we measure improvements in future."
She added: "People do want to know their services are listening to what they want."
Opposition parties say the change of direction is an admission that central targets have distorted clinical priorities and levels of care in parts of the NHS.
Dr Hamish Meldrum, chairman of the British Medical Association, said most people were already seen within two weeks and questioned whether the private sector would have access to the specialist tests and treatments needed for cancer care if patients were sent down that route.
He added: "It is a wee bit of a non-issue."
The two-week cancer target is only expected to affect a few hundred patients because most NHS trusts in England already meet the deadline.
But involving the private sector in acute treatment is regarded as a major change of approach and will prove controversial with unions and MPs on the left of the party who oppose further private encroachment in the NHS.
Currently only elective surgery such as hip replacements and cataract surgery is provided through private treatment.
There are fears among some public service professionals that hospitals could be open to legal action if they fail to deliver on the new range of rights ministers will announce.
There could be financial penalties for failure to keep to the two-week limit which at the moment is only a target.
Earlier this year a study suggested the NHS's Cancer Plan may have helped boost survival rates.
The two-week target was first introduced for suspected breast cancer cases in England in 1999, and extended to all cancers in 2000. It was adopted in Wales six years later.
Harpal Kumar, Cancer Research UK's chief executive, said: "Waiting to see a specialist can be an extremely distressing time for people whose GPs suspect them of having cancer so we welcome this news.
"But as most NHS trusts in England already meet the two-week deadline, we believe the Government will have a greater impact on cancer survival if they focused their energy on improving early detection, when treatment is often milder and more effective."
The NHS in Scotland has had a target since 2001 of 95% of urgent cancer cases beginning treatment within two months of referral.
The same target exists in Northern Ireland.