Former SNP leader and first minister Alex Salmond said he is confident his party will be the overall winners in the local government elections north of the border, but said nationalists "would need to do something" about the surge in support for the Conservatives when the General Election takes place in June.
In the contest for Glasgow - Scotland's largest local authority where Labour has been in power since 1980 - Jeremy Corbyn's party fielded 43 candidates, and it needed all of them to be elected to retain a majority.
But after the first three wards were declared, it became clear Labour would not be able to retain overall control of the council.
The Tories gained a councillor in Shettleston, with Thomas Kerr, 20, saying he was ''shocked'' to win in the east end of Glasgow, a former Labour stronghold.
He put his victory down to opposition to another Scottish independence referendum.
The Conservatives also had a councillor elected in Paisley's Ferguslie Park - the most deprived part of Scotland - for the first time ever.
Clackmannanshire Council, the smallest authority in Scotland, was one of the first to declare all its results - with the SNP remaining the largest party after returning eight councillors, one fewer than in 2012.
Both Labour and the Conservatives had five councillors elected, with the result for the Tories up four on five years ago.
A total of 1,227 councillors are being elected across 32 local authorities areas in Scotland.
As well as targeting an historic win in Glasgow City Council, Mr Salmond said the SNP is also hoping for a majority on Aberdeen City Council.
He told the BBC News Channel: "The SNP are running very strong in Aberdeen, we've got high hopes of taking control of the city. In the shire (Aberdeenshire Council), the Conservative vote is very strong and we'll have to do something about that in five weeks' time.
"The Conservative vote is on the rise, but I think at the end of the day Scotland will be the only place the Conservatives have been beaten - that is to say the objective of an election campaign is to win more votes and more seats than any other party - and we are confident the SNP will do exactly that across Scotland.
"So when it comes to the General Election we want to reinforce this trend - after all there is one thing absolutely desperately needed in this country, a real opposition to Theresa May and the Conservative Party and the SNP in Scotland intend to provide it."
He said it would be a "major moment" for the SNP if it wins power in the "iconic" city of Glasgow, which has been part of Labour's traditional Scottish heartlands.
He added: "Here in the North East of Scotland we're hoping to take control of Aberdeen, which would be also be a major moment, so these are two very important moments.
"But the votes across the country all count and we'll be looking to be the largest party in terms of seats and votes after all the votes are counted today."
With results available from eight of Scotland's 32 councils, the SNP have 69 councillors, with Nicola Sturgeon's party gaining four seats so far.
But the Tories have gained 26 seats, winning a total of 42 councillors. In contrast Labour are down by 23, with 39 councillors elected.