The MSP has warned that the Dutch firm, who took over the service in 2015, that they could be removed from operating the service if the poor service continues.
More than 14,000 people had signed a petition called for Humza Yousaf to take action against Abellio due to the poor service.
The ten year contract has a clause which allows the contract to be ripped up if only 84.3 per cent of trains are on time or less than five minutes late. It had been previously reported that the contract could only be scrapped at the half way point.
Abellio are expected to meet a target of 91.3 per cent of trains arriving on time, however, the group has been falling short with latest figures showing a performance of is 89.6 per cent.
It is understood that if the group falls to meet the 84.3 per cent arrival target for three months in a row, or four months out of 13, then the Scottish government could cancel the arrangement.
Speaking on the issue, Humza Yousaf told the Sunday Mail said: “If the service further declines, there’s a mechanism to terminate the contract early.
“I want improvement and we will use every lever to make sure that we improve our railway.”
“But make no mistake about it, if that improvement is not forthcoming, there’s a reason why we have a break clause in the contract.”
He added: “As someone who uses the train – most of my parliament journeys to Edinburgh are at peak time – I understand the frustrations that people feel.
“There is overcrowding, capacity issues, trains skipping stops, issues around reliability and communication.
“All these are at a level that is unacceptable to me. Abellio have some very ambitious plans for our railways in the future.
“What I’ve said to them is the shiny bells and whistles are great, but now get back to the basics – reliability, capacity.
“Get on to that and make this a good experience for the passenger.”
Although Abellio are not below the require rate for cancellation, Abellio ScotRail managing director Phil Verster stated that delays could continue or worsen as work is carried out to improve the network.