The SNP is seeking to take leadership of a council that has been held by Labour for 26 years.
It comes after the party won 36 seats on North Lanarkshire Council in the local election last week.
Labour, which has controlled the local authority since it was founded in 1996, secured 32 seats.
Meanwhile, the Conservative group on the council was reduced to five councillors, whilst the Greens and the British Unionist Party both won a seat.
The SNP has said that it would be willing to form a minority administration, but made clear that it will not negotiate with the Conservatives.
Jordan Linden, who was unanimously re-elected as the group’s leader, urged Labour to “accept the democratic mandate” given to the SNP.
And he warned Labour against any prospect of working with the Conservatives or the British Unionist Party.
“The people of North Lanarkshire have once again made it clear they want the SNP to lead any administration locally and deliver the commitments we made in our manifesto,” said Linden.
“My group got straight to work on Friday following the count and we have spent the weekend in discussions with likeminded parties to see if we can come together to deliver collectively for the people of North Lanarkshire.
“That Labour, who came second, are trying to cobble together 39 councillors with the support of the Tories and the right-wing BUP is as worrying as it is disgraceful.”
Linden urged Labour to work with the SNP administration to deliver improved services locally.
“The people of North Lanarkshire are angry at Labour’s deal with the Tories for the last five years,” he said.
“They will be furious at the prospect of even more extreme parties being drafted in to run our local services, especially after being roundly rejected at the Ballot Box.
“It’s time for Labour to accept the democratic mandate that has been given once again to the SNP and work with our administration to deliver improved services locally.”
He added: “Whoever ends up in charge of the council will face immediate challenges as trade union Unite has announced it is to hold strike ballots for council employees across Scotland.”