Defending his plans today, he said: "I am taking absolutely nothing for granted.
"My entire focus is on the next 44 days and the General Election, which will decide which team runs this country for the next five years.
"I want that to be me and my team but the alternative is it is Ed Miliband and his team, and that is the focus that I have in the days ahead.
"What I did in my kitchen is I gave a very straight answer to a very straight question and I think that people will understand that - that saying you want to serve a full second term for a full five years is a very reasonable, sensible thing to say.
"So I think we should just focus on the issues at the election about who do you want to run the country for the next five years."
Speaking at a question-and-answer session organised by charity Age UK, he said: "I want to serve the full second term, the full five years as your prime minister.
"But it's not my choice, it is all of your choices, the British public's choice.
"In 44 days' time they get to decide whether I am Prime Minister for the next five years or whether Ed Miliband is prime minister for the next five years.
"I am going to fight with everything I have got to win that election because we have a long-term economic plan that is working, we are putting the country back to work, we have turned the economy around, we have provided, I believe, the dignity and security that elderly people deserve in their old age.
"That is the fight that I am going to have.
"I think giving a straight answer to a straight question about the future is actually a sensible thing to do and I think most people understand that, rather than want to play an endless games of political processes five years hence."
Former Tory Cabinet minister Michael Portillo today described Mr Cameron's announcement as "bizarre".
Mr Portillo told BBC Radio 5 Live: "I think it is bizarre and it has occupied the last day's news. It may even occupy another day's news - I don't know.
"And with only about 44 days to go until the election, if any other member of the Government had taken up the news with an irrelevance like this, I think the Prime Minister would have been very cross.