The “moving annual average”, on which the operator is judged, went up by 0.2 points to 90 per cent in the year to last Saturday, compared to a month ago.
However, it remains 1.1 points below the benchmark level, and ScotRail said it could not predict when it would be back on course.
During the last four weeks from 11 December, 89.7 per cent of trains arrived within five minutes of schedule - the standard measure.
The figure is 2.8 points better than the same period last year, the usual industry comparison.
It is also 6 points better than the previous four weeks.
Transport minister Humza Yousaf described the results as “encouraging” but said there was “still much work to be done”.
Opposition parties said things were still not good enough.
Phil Verster, managing director of the ScotRail Alliance, which includes track owner Network Rail, said: “It is very difficult to pin down when exactly we will be back to benchmark level because of the impact of incidents.
“However, we have improved over the last three periods [months]. That’s a good sign.
“But it’s not victory yet - there’s a long way to go.”
ScotRail said that had come despite three “significant disruptive events” - overhead line problems at Hyndland in Glasgow on 31 December and 6 January, and a child’s scooter thrown onto tracks at Airdrie on 5 January.
The operator said that made it the second best performing large operator in the UK, after Northern, among the six which runs the most trains.
It hailed a “significant improvement” in punctuality over the past four weeks, which included busy Christmas and Hogmanay, one of its busiest periods.
Mr Verster said: ““These latest figures show our performance improvement plan is starting to produce results for our customers.
“We are achieving this in the middle of the biggest upgrade to our railway since Victorian times.
“We can do more and we can go higher, and every single one of the 7,500 people who work on Scotland’s railway is committed to doing just that.
“The sheer scale of the work we are doing to improve the railway has resulted in more disruption than normal.
“I hope our customers can take some encouragement from the continued improvement.
“Later this year, our modernisation work will start to bear fruit.
“The introduction of our new faster, longer, greener trains will dramatically increase the number of seats we have available - and will help us to reduce journey times.”
Mr Yousaf said: “It is encouraging to note performance has improved compared to the previous period and is above the same period last year by quite some distance - 2.8 per cent.
“It also continues to be much higher than the GB average of 87.4 per cent.
“There is, of course, still much work to be done and these figures include several incidents which caused widespread disruption across the network – some of which was outwith the control of the industry, such as vandalism or trespassing.
“However, in areas where the industry can improve, steady progress is being made by the ScotRail Alliance in terms of the improvement plan.
“I expect to see further improvements over the coming months, although I accept some disruption during the winter weather will be inevitable.
“When problems do happen, measures must be taken swiftly to rectify the situation and, crucially, passengers must be kept informed.
“As ever I am grateful to ScotRail staff who are often working in very challenging conditions to lift performance and deliver rail services which passengers deserve.”
Scottish Conservative North East MSP Liam Kerr said: “It’s all fine and well publishing these figures, but commuters know that they are still not receiving a good enough service.
“Every day, they are forced to put up with delayed and overcrowded trains, and many have simply had enough.
“If ScotRail really want to convince passengers the situation will improve, they need to outline the actions they are taking that will make a difference in the immediate future.”
Scottish Labour transport spokesman Neil Bibby said: “2016 was a year of delays and disruption on Scotland’s railways.
“This year needs to be a year of change and improvement.
“Humza Yousaf said he expected ScotRail to hit their performance targets by the end of March, yet here we have another set of figures showing contractual targets are still being missed.
“The clock is ticking for Humza Yousaf and ScotRail.
“Passengers are fed up with delayed, overcrowded and cancelled trains.
“That’s why Labour called for a fare freeze in 2017, which would benefit every single passenger.”