Keith Brown said the Scottish Government would go further than the £50 million pledged to speed up the justice system following the delays caused by the pandemic.
The backlog of Sheriff and High Court solemn cases is expected to last until 2025, with summary trial backlogs lasting until 2024.
MSPs on Holyrood’s criminal justice committee quizzed the minister about the issue on Wednesday.
Conservative MSP Jamie Greene described the backlog as “huge”, saying he had recently spoken to a remand prisoner at HMP Edinburgh whose case had been delayed twice with no prospect of a trial within the next six months.
Mr Greene said: “There are clearly human rights aspects to this, we can’t lock people up indefinitely.
“These are young lives which are possibly being ruined because they’re being stuck in a prison cell for two, maybe three years waiting on their trial.”
Mr Brown said ministers would set out further action in the coming Programme for Government.
He said: “We’re looking to take early action in relation to remand, not least for the reasons you have mentioned.
“We are very conscious of the human rights of those involved.
“Also – if you’ve never experienced the justice system before – the impact it can have on you, your family, your employment and all sorts of things.
“The situation we’re in is arising from the pandemic and like many other jurisdictions we want to do the best we can to mitigate the effects of that.”
Mr Brown had previously refused to put a date on when the government hoped to have cleared the court backlog that had been exacerbated by Covid-19 when questioned on the subject by The Scotsman in June.
Senior lawyers had last month asked for changes like the remote balloting of jurors, meaning only those who will actually sit need to attend court, to become the norm.
In a bid to reduce the backlog, the Scottish Courts and Tribunals Service was planning to introduce four more High Courts from this month, as well as two more sheriff solemn courts and up to ten summary courts.