Rutherford, 25, told BBC Three Counties Radio: "I want to be a double Olympic champion and I think I've got another two in me at least.
"If one of those goes well, that's a great story. It doesn't happen often."
Progression of British record
- Lynn Davies, Berne, 30 June 1968
Chris Tomlinson, Tallahassee, 13 April 2002
- Chris Tomlinson, Bad Langensalza, 7 July 2007
- Greg Rutherford, Berlin, 20 August 2009
- Chris Tomlinson, Paris, 8 July 2011
- Greg Rutherford, San Diego, 3 May 2012
The Milton Keynes athlete struck gold earlier this month with a fourth-round leap of 8.31 metres, but it was the shortest winning leap since Randy Williams of the USA won the 1972 competition in Munich with 8.24. And Rutherford has no intention of resting on his laurels.
"The other thing is I want to jump much further than I have. I'm not happy at all with the distances I've jumped.
"To win the Olympics with 8.31 was surprising. As much as it was enough on the day, I want more and I expect more from myself," he said.
Rutherford's moment of glory at the Olympic Stadium was sandwiched between the gold medal triumphs of
in the heptathlon and 10,000m respectively, on what has become known as 'Super Saturday'.
"I was saying to everybody else, 'You know what, I could go out and win this' and my team were saying, 'Yeah, that would be amazing' - and Charles van Commenee, our head coach, said, 'If you don't come back with a medal, I don't expect to see you tomorrow.'
"It was banterish, but in a way I think he was being quite serious because I was in a great position, I was never going to get a better opportunity in my life," he said.
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