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During the campaign, the Labour leader said he would "deal with" the issue of graduates burdened with debt since tuition fees rose to £9,000.
He told the BBC he had never promised to abolish all debt as Labour "were unaware of the size of it at the time".
Tory MPs have accused him of misleading students and urged him to apologise.
Historical levels of student debt in England since tuition fees were introduced rose to £76.3bn last year and senior Labour figures have said an across the board debt moratorium could cost in the region of £100bn.
Many believe Labour's pledge to scrap university tuition fees for future undergraduates and help existing students was one of the factors behind its better-than-expected election performance last month.
An unexpectedly large turnout among students helped Labour win seats such as Canterbury, which it took for the first time in 100 years, and increase its majority in cities such as Cambridge, Bristol and Leeds.
Mr Corbyn has been accused of using students as "election fodder" after he claimed during the campaign that he would also look at ways to lengthen the period of paying existing debt off or "some other means of reducing that debt burden".
He told the music and lifestyle title NME he didn't see "why those that had the historical misfortune to be at university during the £9,000 period should be burdened excessively compared to those that went before or those that come after".
In recent weeks, senior Labour figures have distanced themselves from talk of a debt amnesty, saying that while it remains a long-term ambition, they do not yet know how it could be funded.
Speaking on the Andrew Marr show, Mr Corbyn said his remarks during the election did not amount to a "commitment" to erase student debt and the party would be expanding on its position in the near future.
"I did not make a commitment we would write it off because I couldn't at that stage," he said.
"I pointed out we had written the manifesto in a short space of time because there was a surprise election but that we would look at ways of reducing that debt burden, recognising that a lot of it is never going to be collected anyway and try and reduce that."
"We never said we would completely abolish it because we were unaware of the size of it at the time," he added.
Under the current system, loans that are not repaid after 30 years are written off for graduates who began their degree courses after 2012 and after 25 years for those who studied between 2006 and 2012.
Recent research from the Institute for Fiscal Studies suggested students in England are set to graduate with average debts of £50,800, with many poorer students incurring much higher sums.