Glasgow MSP Anas Sarwar said Labour in Scotland suffered the "worst result" in its history when its share of the vote slumped to just 9% in the European elections last week.
In the wake of that defeat, he said Labour must be an "unequivocally Remain" party - and also called on leaders Jeremy Corbyn and Richard Leonard to tackle infighting and do more than "speak for a clique or faction" within the party.
Mr Sarwar lost out to Mr Leonard in the contest to succeed Kezia Dugdale as Scottish Labour leader after she quit in 2017.
Following the party's poor performance in the European elections, Mr Leonard said he "hoped" Scottish Labour would back a second Brexit referendum in all circumstances, and he would campaign for the UK to stay part of the European Union.
Members of the party's Scottish executive committee will decide whether to adopt this as official policy when they meet on Saturday June 8.
Arguing Scottish Labour should be an "unequivocally Remain party" and an "unequivocally pro-UK party", Mr Sarwar said the "radical" programme Labour is putting forward in other areas will only get a hearing from voters if the party is "clear on the biggest issues of our day".
In a letter to Labour members in Glasgow, he said: "The Scottish Labour Party needs to urgently take a look at itself and change if we are to ever compete, never mind be the party of Scotland again."
He insisted "factionalism and division" within the party "needs to stop".
Two Labour frontbenchers at Holyrood quit their posts this week, with Neil Findlay stepping down as constitutional spokesman and Daniel Johnson resigning from the justice brief.
But Mr Sarwar said the party needs to come together, arguing: "We can only advocate unity to the country if we demonstrate unity in our party.
"That's why the factionalism and division needs to stop. That is a responsibility for all of us, but the culture is set at the top and leadership must come from there too.
"Rather than showing humility and reaching out, it's deeply disappointing that those responsible for the election campaign have chosen to lash out and attack their own colleagues."