The council leader argued there were “well-functioning” Labour and SNP coalitions currently operating across Scottish council areas.
Speaking at Perthshire Football Club in the Possilpark area of Glasgow on Tuesday, Sir Keir also rejected calls for a coalition agreement on a national level.
He said: “Going into the general election, let me be absolutely clear, no deal going into the general election and no deal otherside. I could not be clearer about this.”
Joining his UK colleague in the coalition rejection, Scottish Labour Leader Anas Sarwar said the “whole point” is to get Susan Aitken “out” as she “is a disaster for Glasgow”.
There are currently SNP Labour and SNP administrations in areas such as Edinburgh, East Renfrewshire, Stirling, Dumfries and Galloway and Fife.
Asked if local authorities in SNP and Labour coalitions were “bad deals”, Mr Sarwar: “This is an opportunity for us to change how we do local democracy, change how we do local government. I think both the SNP and Tories are bad for Scotland and the UK and therefore I want to deliver no calls for either so no coalition.”
The SNP came into control of Glasgow in 2017, however, leadership has faced severe public outcry over waste and cleanliness issues including industrial action taken by refuse workers.
Closures of certain public council-run services including libraries and leisure facilities as a result of Covid have also caused discontent with the council’s administration.
Asked by The Scotsman if UK Labour could leave Scotland behind as a result of support for Scottish independence, Sir Keir said: “I think UK Labour and Scottish Labour are speaking with one voice on this.
"We believe in the union, we believe in the United Kingdom but there is also a question of priorities.
"When so many people are struggling with the cost of living crisis and when so many people want to see something better coming out of the pandemic to just revert back to the old arguments and old divisions in wrong.
"I think the priority should be on building on what we achieved in the pandemic which is communities of people coming together and supporting each other.”
Over claims that 25 Labour candidates support independence, Mr Sarwar said this is “not true” and 21 out of 25 have said these are false claims.
Asked about the SNP's record in power, Starmer said: "The SNP do what they always do - which is to try to use the constitutional issue to mask their own failures.
"You don't need to scratch away much when it comes to wages, health and education of people in Scotland to see the failure that is the SNP Government.
"The distraction tactic, only speaking about the constitution when people want to know how they are going to pay their energy bills, is not going to work.
"I think, as Labour puts practical plans on the table, it's becoming increasingly clear that we are the party with answers to the issues that are uttermost in people's minds."
On the SNP’s focus on independence in Scotland, Mr Sarwar said: “Nicola Sturgeon wants to pretend this is all a Scotland versus England thing but actually if you go to Birmingham, Manchester, Liverpool, Cardiff, London they feel distant from Boris Johnson and the Tories as well.”
On nuclear power, Sir Keir said he did not understand why the SNP does not follow the lead of Labour on the aim to “fast-forward” on nuclear to tackle the cost of living crisis through energy security.
Mr Sarwar agreed, saying he wants to see Scotland to “supercharge” its investment in renewables but said a “diverse mix” including nuclear was needed.
The Scottish Labour leader said such a plan would “create lower bills and more jobs in the longer term”.
During the visit, 21-year-old Lauren MacDonald, who is a spokesperson for the Stop Cambo campaign, questioned Starmer on his commitment to tackling the climate crisis.
It comes as UK Labour has called for nationwide injunctions to block Just Stop Oil demonstrations, arguing demonstrations by the environmental activists have caused “misery” for motorists.
The climate activist approached both leaders in Glasgow after Mr Sarwar said he thought “we are living in a climate emergency” and “time is running” out to take urgent action.
He said: “People should have the freedom to protest within the measures of the law.”
Yet, the young climate activist was abruptly walked away from when she told the UK Labour leader she is currently experiencing stress-induced hair loss as she emphasised her and other young people’s futures “currently do not exist” as a result of the crisis.
Ms MacDonald said: “Starmer and the Labour party are not doing enough about this. The way that young people feel today is complete terror and I am genuinely so terrified about my future.
"I feel what I got was a standard politician response saying thank you and running away. He did not actually feel my pain and think what can I do more and I’m not seeing any of that in the UK Government.”
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