Frontrunner Kezia Dugdale has said the party won’t win again in Scotland without recapturing its lost support base in the city.
But Ken Macintosh, the Eastwood MSP, says this sends out the “wrong message” and is “insulting” to Glaswegians.
Leading public sector union Unison backed the Ms Dugdale candidacy.
Ms Dugdale and Mr Macintosh took part in a hustings in Glasgow last night.
The city was once a Labour stronghold, but the party was wiped out by the SNP in last month’s UK election. Glasgow was also labelled “Freedom city” by Alex Salmond after it voted Yes for independence in the referendum.
“The Scottish Labour Party was founded in Glasgow,” Ms Dugdale said.
“We won’t be able to get back on our feet without this great city’s support. To put it bluntly, Labour won’t win again without winning in Glasgow.
“The general election wipeout we suffered here was years in the making. Despite the hard work of our candidates, councillors and activists, the majority of people in Glasgow had decided who they wanted to represent their hopes and aspirations – and it wasn’t Labour.”
The 33-year-old said new housing, investment and a “melting pot of new cultures” means Glasgow is a city transformed.
And she warned: “The people here have left the Labour Party behind. We need to transform ourselves to keep pace with Glasgow. We should use the motto of the city as our guiding principle – People Make Glasgow.
“Only when people look at the Labour Party and see themselves reflected back will we have a fighting chance again.”
But Mr Macintosh said this is the “wrong message”.
“We need to broaden our appeal to the whole of Scotland. I want to win Glasgow, but this sends out the message that Glaswegians should vote Labour out of some sort of loyalty to the past – it’s insulting to most Glaswegians.
“I want to broaden our appeal to people – this reinforces the stereotype that we’re the party of west and central Scotland.”
Mr Macintosh says Labour must look beyond its “industrial past” and appeal to the 75 per cent of Scots working in the private sector.
It came Unison announced it is endorsing Ms Dugdale to its members and the Cowdenbeath MSP Alex Rowley for deputy leader. Unison Scotland Labour Link Chair Gordon McKay said the party must “change direction, start listening to its friends and pursue policies that will win the support of working people”.