The row erupted on the day terror attacks wracked the Belgian capital, Brussels.
In a dispute over proposed cuts to disability benefits, John McDonnell called on the Chancellor to resign, calling him a “political chancellor” and accusing him of “grubby, incompetent manipulations”.
But Tory MPs hit back, asking whether it was appropriate for the Hayes and Harlington MP to question the integrity of George Osborne, considering he had suggested at a 2003 meeting that IRA “bombs and bullets” had helped bring about the Northern Ireland peace process.
James Cartlidge, the Conservative MP for South Suffolk called on Mr McDonnell to “withdraw your previous support for terrorist organisations that have attacked this country”.
Mr McDonnell described the comments as "unacceptable" and replied, "You have heard me share the sentiments of the whole House on the issue of Belgium".
Tom Tugendhat, a former army officer, said Mr McDonnell had stood alongside terrorists who murdered his friends.
“You have called into question the morality of the leadership of the Chancellor,” said the Tonbridge and Malling MP, adding, “Will you please discuss with this House the morality that allows you to stand with bombers who murdered my friends in Northern Ireland and question the integrity of the Chancellor?”
Mr McDonnell had been responding to George Osborne’s speech in the Budget debate.
He said he believes the behaviour of the Chancellor in the last 11 days “calls into question his fitness for the office”.
"I also believe that it certainly calls into question his fitness for any leading office in Government,” he added.
The Labour front bencher accused Osborne of “personally forcing through the cuts in PIP (personal independence payment” which he said for many disabled people “actually make life worth living”.
He added, "The Chancellor was willing to cut away this vital support to some of the poorest and most disadvantaged people of our community.
"Do not tell us we're all in this together."