ANAS Sarwar says Scottish Labour are "aspiring" for first place ahead of this week’s elections.
The party leader, while acknowledging an overall first place finish will “probably” be out of reach, says he hopes to see “progress” in the ballot.
Polls have been encouraging for Labour in Scotland, who are forecast to overtake the Tories.
A study by Survation released in early April found 23% of the 1002 Scots asked said they would give their first preferences to the party.
Another Panelbase poll for the Sunday Times, released at the weekend, found 24% of the 1009 Scots surveyed would vote for Labour, compared to 21% for the Tories, when undecided voters were removed. The SNP remained out in front on 42% of first preference votes.
But the Labour leader said he hoped any “progress” shown on Thursday could spur the party to a win in the next General Election and see them compete with the SNP at the next Holyrood vote in four years’ time.
“I’m taking nothing for granted. The mood music has been good, I think we ran a very strong campaign, obviously, it’s still a few days to go, and we’ve got a strong message to people,” he told the PA news agency.
As well as an election on local issues, Sarwar said it was also an “opportunity to send a message to the SNP and the Tories that they’ve got to recognise the scale of the cost-of-living crisis and take the appropriate action”.
“The polls are encouraging, but the poll that matters is the poll on May 5,” he continued.
“I don’t aspire for second place, I aspire for first place and that’s probably too tall an order in the next few days given the project that we’ve had in the past year and the work we’ve got to do moving forward.
“I want us to demonstrate progress, I want us to demonstrate we’re moving forward and I want us to be in a position where at the next general election we have a genuine opportunity to boot out Boris and elect a UK Labour Government and come the next Scottish Parliament election where Labour is competing in that election to win.
“That’s the ambition and that’s the plan, and this is a moment for us to demonstrate that progress.”