It is intended that internships will at least improve participants' skills and experience and may in some cases lead to full-time work.
They will be paid at a rate only slightly higher than undergraduates' income from grants and loans, according to the Telegraph.
Mr Denham told the paper: "At the end, they will be more employable, and some of them will get jobs. Employers won't want to let good people go.
"These are the children of the baby-boomers. They will be a very big group. What do we do with them? We can't just leave people to fend for themselves."
Although welcoming the move, the Conservatives said it was not enough.
Shadow skills secretary David Willetts said: "A small number of businesses taking on graduate interns is welcome but this does not match the scale of the crisis facing young people trying to find jobs.
"That is why we have proposed focusing more than £500m in the 'train-to-gain' program, on helping young people get apprenticeships and worthwhile job opportunities."
Universities have reported that firms have been cancelling spots on the annual "milk round" - when employers visit universities to recruit students - or simply focusing on elite institutions.
In the same interview Mr Denham declined to comment on suggestions the government could bring forward plans to raise the school-leaving age to 18.
A new requirement for youngsters to remain in education or training until they are 18 only currently applies to those aged 11 or under this year.
Here are some of the comments you've sent us:
I am currently in my last semester at university doing a BA (Hons) Tourism Management degree. I think that this new scheme will be a great way for graduates to at least get into the world of work and keeping fingers cross that it is related to what we are all studying and with all the knowledge be able to be a good asset to a company.
David Scott, Witham, Essex
I graduated in July 2008 with a languages degree and despite my best efforts I still find myself without work. I am beginning to feel increasingly despondent at my lack of success in securing a job and frustrated by the dearth of opportunities and provision for recent graduates. I have in previous years claimed Jobseekers' Allowance but found the experience demoralising and for all intents and purposes rather useless. The proposal to offer internships seems to be a step in the right direction but still somewhat limited in efficacy as it holds no guarantee of a stable, long-term position.
I graduated from my university in December of last year. After receiving my diploma I received this word of advice "congratulations son you did it, now just remember your walking into the worst economic situation in eighty years, now good luck!" and don't forget my pat on the back please. I have worked my entire way through schools in restaurants and now that I have graduated there is no way you could make me give up my job, because there is not a better one to be found. No job fairs, no internships, and the new favourite corporate word in America right now "hiring freeze" So much for the American dream today maybe I will try again tomorrow.
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