In a speech in northern England, Cameron later said his government's plans to hack back a record peacetime budget deficit over the next five years would enable interest rates to stay lower for longer, save the recovery and also ease inflationary pressures.
Cameron's concerns about rising inflation appear to contradict assurances from the Bank of England that a recent spike — it was nearly double the 2 percent target in April — is temporary and will subside over the coming year.
"Policy set independently by the Bank of England, that is the right way to do things," the Conservative leader told GMTV.
"We have seen a slightly worrying increase in inflation in recent months so interest rates will be set to control inflation."
Cameron, who became prime minister earlier this month after forming a coalition government with the smaller Liberal Democrats, has been outspoken about monetary policy in the past — an area usually avoided by government ministers.
At the Conservative annual conference in October 2009 Cameron said "printing money leads to inflation".
In November, the BoE increased its quantitative easing program, under which it bought assets with newly-created cash — to 200 billion pounds to help drag Britain out of its worst recession since World War II.
Earlier this week the OECD said the BoE must raise interest rates earlier than previously thought and no later than the fourth quarter of this year due to the gradual drift up of some measures of inflation expectations.
However, if the BoE raises interest rates to contain inflationary pressures, analysts say there will be little to protect the still frail economy from the sweeping government spending cuts the Conservatives have talked about.
In his first major speech since taking office, Cameron said the coalition's emergency budget on June 22 would outline how the deficit — running close to 11 percent of gross domestic product — would be dealt with over the next few years.
He warned that failing to take action now would kill off Britain's recovery from the worst recession since World War II.
"Our budget deficit is set to overtake Greece," Cameron said in a speech to business leaders in Saltaire, northern England. "If we don't deal with this, there will be no growth, there will be no recovery."
"Getting the deficit down and keeping it down will ... allow interest rates to remain lower for longer."
Cameron said he believed Britain could rebalance economic power, lower taxes, inject new life into the private sector and move to an economy built on savings and investment rather than debt.
He also said he was glad to see a growing international consensus on the need for some form of banking levy.
The coalition outlined this week 6.2 billion pounds ($8.9 billion) of spending cuts this year.
Cameron inherited an economy just emerging from deep recession. The Office for National Statistics said this week the economy grew by 0.3 percent in the first quarter, up from an initial estimate of 0.2 percent.
