Mr Sarwar said Douglas Ross needed to “grow up” to ensure that the people of Scotland’s lives were “front and centre” of campaigns for the Holyrood elections in May.
The comment from the leader of Labour party in Scotland comes after Mr Ross wrote a letter seeking an “open discussion” about cooperation between the Scottish Conservatives and Scottish Labour to fight “threat of independence.”
The proposal was offered to Willie Rennie, leader of the Scottish Liberal Democrats who also refused.
Mr Ross said the reason for writing to the leaders was to focus on the “national recovery from coronavirus” and “not another divisive independence referendum."
In his letter, the Tory leader invited Mr Sarwar to pledge that he will vote against a second independence referendum regardless of the result in May’s election, rule out a coalition or confidence deal with any party who seeks an independence referendum in the next parliament and agree to form a pro-UK anti referendum.
He wrote: “As much as we would like to spend the next six weeks debating our national recovery plans, there will be no recovery if there is a nationalist dominated Scottish parliament single-mindedly focusing on securing independence.
"We must first defeat this fresh drive towards a second independence referendum.”
However, in an interview this morning, Mr Sarwar said: “I mean, I don’t know how many times he needs me to say it- Douglas, grow up.
"We’re not in the playground, this is not a game, this is people’s lives.
"Let’s put people’s lives front and centre of this campaign so we can deliver a covid recovery parliament that’s not obsessed about independence, not obssessed about a referendum, not obsessed about an Alex Salmond and Nicola Sturgeon fight.
"But also not obsessed about fighting in the constitution like Douglas Ross is or obsessed about going back to that failed system pre-covid.
"But is instead obsessed about getting rid of poverty. It’s obsessed about rebuilding our NHS, it’s obsessed about putting our education system as a global beacon again.
“That’s what I’m obsessed with: making sure we have a national recovery plan that delivers for the people of Scotland.”