The boost on what is now the operator’s busiest day of the week brought the daily total to a new high since the start of the Covid crisis in March last year.
Overall, ScotRail’s passenger numbers increased to 40 per cent of normal in the week to last Sunday compared to just 10 per cent three months ago.
People’s apparent growing confidence to travel is also reflected in the number of over-60s and others using their free bus passes, which has climbed to 55 per cent of normal.
Ferry and car travel in Scotland last week was only 5 per cent below pre-Covid levels, but air travel was down by 70 per cent.
However, ScotRail operations director David Simpson told The Scotsman he expected passenger numbers to return to only 80 per cent of normal over the next three years.
The company is running 82 per cent of its normal services and this is only expected to be increased to around 85 per cent in December and nearly 90 per cent next May.
Mr Simpson said current services were “more than sufficient to cope with the demand levels we expect to see through the summer and autumn”.
He said: “We have seen a healthy growth in recent weeks coinciding with the easing of lockdown restrictions across Scotland.
"We are seeing passengers return, but we’ve yet to see any marked return of commuter traffic.”
Mr Simpson predicted there would be fewer five-days-a-week commuters but more flexible working and leisure, tourist and off-peak travel.
He also hoped record punctuality achieved during the lockdowns would continue as more passengers returned.
He said: “We have analysed to death how trains are performing and have built the lessons from that into the current timetable to make it more resilient.
"We have refined the timetable to make it more robust and reliable.
"Even though we have seen an increase in passenger numbers, we have still maintained those high levels of performance.”
A spokesperson for the Scottish Government’s Transport Scotland agency said: “While we have seen some welcome return to rail, we are still some way off the previous record numbers of passengers.
"We are working closely with industry partners to keep essential services moving, while at the same time monitor passengers trends and plan for future timetable changes.
“As we emerge from the pandemic, it is clear from the financial challenges we face that we will need to re-evaluate how we deliver services, including ticketing and stations, to ensure they provide the best value for the public purse, while meeting demand and encouraging future growth.”