The party has written a letter to Deputy Prime Minister and Communities Secretary Angela Rayner, in which it also urged the government to send in private sector binmen.
The long-running strike is continuing, with rubbish piling up on the city’s streets, despite talks aimed at ending the pay dispute.
Members of the Unite union met with Birmingham City Council on Thursday, but the talks have so far failed.
Unite says the dispute will not end unless the “hugely damaging” cuts to bin collectors’ wages are reversed.
But Birmingham City Council says the aim of the restructuring is to create a “modern, sustainable and consistently reliable waste collection service”.
Shadow communities secretary Kevin Hollinrake and shadow Cabinet Office minister Alex Burghart have called on the government to hold a COBRA meeting to respond to the dispute.
The Tories said the meeting would “ensure that there is a co-ordinated response between national and local government”.
The government sent in commissioners to oversee Birmingham City Council after it effectively declared bankruptcy in 2023.
In their letter, Mr Hollinrake and Mr Burghart also said the commissioners should “cut the pay of local councillors and redistribute the funding to local services”.
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Last week, environment minister Mary Creagh told the House of Commons that resolving the strikes was a “matter [for] the council”.
She added that both parties needed to “sort this out for the benefit of the people of Birmingham”.
