Humza Yousaf has insisted he is committed to his role as Transport Minister following calls for him to be removed from the post.
The train drivers' union Aslef has urged First Minister Nicola Sturgeon to sack Mr Yousaf over what it described as a "rail crisis" in Scotland.
It follows recent concerns over the performance of train operator ScotRail and serious disruption on Scotland's rail network in the central belt on Thursday.
The Transport Minister said on Friday that he is "certainly not" stepping down, and is monitoring daily a performance plan set up for the train operator.
Speaking as he monitored the morning commute on Friday, Mr Yousaf told BBC Radio Scotland: "My job is to make sure that the railways are running, to make sure that buses are as efficient as possible, to make sure our trunk road network is moving.
"I'm committed to doing that job, as you'd imagine I am. I'll be monitoring things absolutely closely.
"Yes of course there's an apology there for commuters that were disrupted yesterday but an assurance from ScotRail, from me, that we're monitoring things closely and I expect improvements to happen and happen immediately."
A train breakdown in Edinburgh on Thursday morning caused travel woes for commuters.
Ms Sturgeon apologised for the disruption after Scottish Labour leader Kezia Dugdale raised the issue at First Minister's Questions.
The train broke down between Waverley and Haymarket stations, which ScotRail told the First Minister was "probably the worst place in the country" for it to happen.
The incident was the latest in a string of performance problems to hit the rail network, which forced ScotRail to produce a performance improvement plan in September at the request of Transport Scotland after punctuality and reliability fell below target.
Ministers have warned ScotRail it could lose the contract if train performance does not improve.
Mr Yousaf told the BBC's Good Morning Scotland programme: "Everything is under review. If performance declines to 84.3% and that happens for a few consecutive months, then that option to terminate the contract is there. I don't think we're at that stage, but certainly all options are on the table."
The minister monitored ScotRail operations and talked to passengers during the Friday morning commute at Glasgow Central and Glasgow Queen Street stations.
Overnight ice had caused some disruption on the network, but things otherwise appeared to be running relatively smoothly, he said.
"We don't seem to have a repeat of yesterday's incident, which is pleasing to see," he added.
"I've been talking to passengers and there's a lot of reassurance out there that I've been giving that things are going to be getting better on our railways."
A spokeswoman for the ScotRail Alliance said on Friday: "We hosted Transport Minister Humza Yousaf this morning when he visited to see our operations through the peak at Glasgow Central and Glasgow Queen Street stations.
"Everything went well as all our staff are passionate about and committed to driving performance to improve.
"We're in the midst of a period of immense change as Scotland's railway undergoes the biggest improvement since Victorian times."
Phil Verster, managing director of the Alliance, has already pledged to learn from the Edinburgh breakdown and apologised for the disruption.
Charlotte Twyning, Abellio UK's director of policy, strategy and communications, said: "Our people are working hard with our clients, Transport Scotland and the Scottish Government to improve the railway during one of the most significant periods of investment ever undertaken.
"We are using our position within the ScotRail Alliance to encourage Network Rail in particular to ensure that the impact of their work to modernise the track and associated infrastructure does not adversely affect passenger services and that we put the interests of customers above all others."
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