Scottish Labour leader Richard Leonard said the party plans to take action, saying there is "no place" for the "profit motive" on the railway.
Earlier this month, the Scottish Government put plans in place to run the railways as an "operator of last resort" if ScotRail's performance fails to improve.
In February, ministers handed ScotRail its second improvement notice in less than two months after passenger satisfaction plunged to its lowest level in 15 years.
Speaking at the Labour Party's annual conference in Brighton, Mr Leonard said there should be public ownership of public services.
He said there is "no place" for the "profit motive" in bus services, prison service or in the asylum system.
"It should have no place in our railways either, which is why I am today announcing that the Scottish Labour Party will force a vote in the Scottish Parliament as early as next week to end the Abellio franchise of ScotRail," he said.
Mr Leonard also said Brexit is showing the British constitution is "creaking and out of date", adding there is a need to extend democracy to workplaces and communities.
He said the party would push for the abolition of the House of Lords, saying it should be replaced by an "elected senate".
"It s not just more powers coming to Scotland that we need, it is a fundamental rebuilding of the broken British state that is required," Mr Leonard said.
"So that is why we are proposing, at last, the abolition of the House of Lords.
"I believe that its replacement with an elected senate of the nations and regions, built on a federal settlement, would begin the process of reshaping our while political system."
He added: "These changes will have to be worked for and the people won over but we must be confident.
"Confident in the democratic tradition which we inherited. Confident in the socialist ideal which drives us, confident in these practical ideas for radical reform.
"We are on the brink of something extraordinary.
"A socialist Britain will do far more to improve the lives of the people than a separate Scotland ever could."
He called for unity behind Labour leader Jeremy Corbyn, and warned there would be no "shortcut" to a Labour Government "through the SNP"