Miliband's appearance followed a televised election contest on Thursday that Cameron was judged to have won, although not by a big margin, a poll showed.
Labour got a 1 million pound ($1.5 million) boost to its election coffers on Friday from Britain's largest trade union, Unite. The donation drew an immediate reaction from the Conservatives, who accuse Miliband of being in the pocket of union barons.
Polls show centre-left Labour is more trusted by voters than Cameron's centre-right Conservatives on the future of the NHS.
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The Conservatives deny Labour charges that they are bent on privatising the service. Funded from taxation, it is free at the point of treatment, but the system is coming under increasing strain from a range of factors including a growing population, increased life expectancy and expensive new treatments.
The Conservatives said Miliband's plans showed he was "incompetent", saying the strength of the NHS was linked to the strength of the economy - an area where the Conservatives are more trusted than Labour.
Miliband pledged Labour would prevent contracts being forced out to private tender and would introduce a 5 percent profit cap on all outsourced contracts worth more than 500,000 pounds.
The promise is aimed at easing fears among some voters that outsourcing treatment to private firms is a step towards introducing charges for patients. The government says 6 percent of the NHS budget is currently spent on private providers.
"It's right to say that when private sector companies are involved, we don't get excess profits, which is draining money away from the National Health Service," Miliband said.
Nevertheless, the policy risks inflaming latent tension with the business community, who fear Miliband's plans for a more hands-on approach to regulation in sectors like banking and energy could make Britain less attractive to investors.