Mr Corbyn said the "law must apply to everyone" and denied there was a discrepancy between the investigations into soldiers after Republican suspects were sent "comfort letters" offering effective immunity from prosecution.
Earlier this week, the Public Prosecution Service said there was enough evidence to prosecute a man, known as 'Soldier F', for the murders of James Wray and William McKinney at the civil rights march in Londonderry in 1972.
Speaking on Sky News' 'Sophy Ridge on Sunday', he said: "The law must apply to everyone, and I don't think we should have statutory limitations on this."
Mr Corbyn said "we should have a fair and proper judicial process" and said what happened on Bloody Sunday was "awful and appalling". He added:
"I do think it's important to have the independence of a legal process, and there has to be an insurance that everyone has to abide by the law."
He was pressed on whether it was fair given how those members of the IRA suspected of crimes were offered an amnesty in the Northern Irish peace process.
The Labour leader replied: "The Good Friday Agreement was important, seminal and complicated, but it does not provide complete immunity for everyone, it was never intended to."