After a landslide victory north of the border in the 2024 general election, Scottish Labour had high hopes of challenging the SNP in May’s Holyrood election.
However Alexander admitted recent polls were looking “tough”, with Labour slipping behind Reform into third place.
Alexander is co-chair of Scottish Labour’s election campaign with deputy leader Jackie Baillie, who has backed Sarwar’s call for the prime minister to quit.
A senior party source told BBC Scotland News this arrangement would continue despite the co-chairs taking opposite sides in the debate over Starmer’s future.
At a press conference on Monday, Sarwar criticised the appointment of Peter Mandelson as UK ambassador to the US, despite his links to convicted sex offender Jeffrey Epstein.
The Scottish Labour leader said his decision to call for Starmer to go was “not easy and not without pain”, adding that the prime minister was a “decent man” but that his “first loyalty” was to Scotland.
With the election looming, Sarwar said he needed to “decide what I’m willing to accept and what I’m willing to tolerate”.
He added that the UK government’s achievements had been “drowned out” by successive scandals.
Sarwar has not spoken to the media on Tuesday, but posted a campaign video on social media saying Scotland “could not risk a third decade of the SNP in power”.