Nearly 14,000 people have called for ScotRail operator Abellio to have its contract terminated early if performance does not improve.
The online petition puts added pressure on the firm to reverse its worsening punctuality after The Scotsman revealed last month that ministers had demanded improvements.
The worst performing lines include to Ardrossan - where only about one in ten trains arrive within a minute of time - and to Milngavie and Wick (one in four).
ScotRail is also suffering from increasing overcrowding as passenger numbers increase but new fleets of trains are still at least a year away.
It carries more than 7 million passengers a month, which has increased by one third over the last decade.
The company’s ten-year franchise to 2025, which started last year, can be ended in 2022 if it fails to meet targets.
The petition is expected to be presented to transport minister Humza Yousaf at the SNP conference this weekend.
It stated: “ScotRail bosses have been providing a poor service for months and the Scottish Government could be finally about to get tough on them.
“We can give Humza Yousaf the push he needs to take a hard line with ScotRail.”
The latest figures showed ScotRail’s combined punctuality and reliability was 90.8 per cent in the four weeks to 17 September. It compares to a target of 92.5 per cent.
The “public performance measure” comprises the proportion of trains arriving within five minutes of schedule and the proportion which run.
ScotRail would say only the problems were caused by a “variety of factors”.
It has previously blamed bad weather last winter, and having to add extra carriages to Fife-Edinburgh trains from other lines during the closure of the Forth Road Bridge last December.
Scottish Labour transport spokesman Neil Bibby said: “The number of signatures on this petition shows just how disgruntled passengers are with ScotRail services.
“It is time for the minister to explain to passengers what improvements he is going to make and when these improvements will take place.”
Mr Yousaf called for improvements last month when he said performance on the Borders Railway was “unacceptable”.
He said yesterday: “ScotRail’s performance this year has not been at the level the Scottish Government demands and expects, which is why I have taken decisive action in calling for the operator to deliver an improvement plan outlining how they will improve passenger services.”
Phil Verster, managing director of the ScotRail Alliance, which includes track owner Network Rail, has promised to turn things around.
He has told MSPs: “We have submitted that improvement plan to the Scottish Government and we will deliver on it.
“We are in the same space as the Scottish Government - train service punctuality will have to improve, and we are committed to ensuring that.”
The plan involves reducing train breakdowns and track faults.