A letter signed by Lib Dem councillor Martin McCabe to Worthing mayor Lionel Harman said it was 'crucial' councillors heard Worthing Borough Council leader Dan Humphreys' comments and strategy for reversing the spike.
The letter has since been backed by fellow Lib Dem Bob Smytherman and all 10 members of Worthing's Labour group.
Martin said: "I'm delighted that the Worthing Labour Group have backed me on this. My call for an extraordinary meeting of the council is a cross-party effort to ensure everyone is completely informed on this council's strategy for tackling Covid-19.
"This is exactly what extraordinary meetings are for. I urge the mayor to grant this request so that all councillors can hold the executive to account for the good of the public."
Martin's letter comes after a spike of coronavirus cases last week which saw the infection rate rise to more than twice the national average.Both West Sussex County Council and Worthing Borough Council said the outbreak had been swiftly brought under control and the infection rate has fallen significantly over the last few days.
But Martin argued the rise in cases still requires scrutiny of the council's strategy and an 'extraordinary crisis needs an extraordinary meeting'.
An extraordinary meeting is a meeting of a public body that occurs at an irregular time.
The letter read: "As mayor, I know you take your duties with the utmost commitment, thoughtfulness and sincerity.
"You are the conscience of the council.
"I know you are dedicated to catering for the debate of matters of concern to the local community and remaining neutral so that Members who are not on the Executive are able to hold the Executive to account.
"Formally, I believe my request needs five signatures.
"Myself and Cllr Bob Smytherman are requesting that our fellow Councillors respond and join us in this call for an extraordinary meeting of the council. This is an urgent cross-party matter.
"If this doesn't meet the requirements for an Extraordinary Meeting, then surely nothing ever will?
"I urge you to do the right thing."
Councillor Lionel Harman has been approached for comment.