The meeting, to decide how to use £6 million of Scottish Government funding, was called in response to pressure from the opposition SNP group.
However, the Labour administration and other parties have called for the meeting to be postponed in line with recommendations from council and NHS officials.
Four elected members are currently self-isolating and around 100 people would be required to attend the meeting in Motherwell.
Council leader Jim Logue said: “I’m saddened that at a time of great uncertainty and worry for so many residents of North Lanarkshire, that all elected councillors cannot agree to unite when it matters most.
“It is unquestionable that the COVID-19 outbreak will require the council to draw on every resource it has in order to mitigate against the health, social and economic effects of the virus.
“I would urge those who still seem to be playing politics with this issue to think again and agree that any and all monies possible should be used to protect the health of the residents of North Lanarkshire.”
Commenting on the decision to proceed with the meeting, SNP group leader Councillor Tom Johnston said: “The SNP Group will never play politics with issues as important as the current COVID-19 crisis and any statement claiming such is wrong and frankly irresponsible.
“It is true that the SNP Group do wish to see Thursday’s Special Full Council Meeting proceed – especially as Policy and Strategy is set to proceed immediately before it. We fully believe that the until we have direction to suspend all council business, we will continue carrying out our democratic duty.
“On Thursday we can choose to make decisions that positively impact our community now and into the future; whilst Kilbowie and car parking are well known and will still be relevant, following the conclusion of this crisis.
“We believe it is so important to come together and vote to deliver free community alarms for the most vulnerable in our communities who are sadly most likely to be impacted by recent events and also to inject an additional £0.5 million of additional funding to Health and Social Care.
“We made representations to other groups in the council to consider postponing the special council with a common sense approach that areas highlighted such as charging for community alarms be frozen from further action until the worst of the crisis had been dealt with. This was refused by Conservatives and Labour.
“That is why we believe the meeting should take place on Thursday – to continue to deliver for the people of North Lanarkshire.”
He added: “I want to thank the incredible staff of our National Health Service across Lanarkshire for their hours of dedication until now and indeed for the weeks and months ahead.
“I also pay tribute to the Staff of North Lanarkshire Council for leading in Business Continuity and Resilience activity. We shall overcome this by working together.
“I welcome the £320 million injection from the Scottish Government to support businesses during the 2020-21 financial year to assist with Coronavirus Impact and I know that the Scottish Government through COSLA will continue to work with local government, including, North Lanarkshire Council throughout the weeks and months ahead – as we work together to tackle this extremely challenging issue.”
Conservative group leader Meghan Gallacher added: “A meeting took place on Monday between all political groups and council officers to discuss the requested full council meeting. It was suggested by the chief executive that in light of the coronavirus outbreak, that the additional £6.045m should be allocated to help protect residents of North Lanarkshire and council services.
“A collegiate agreement was sought, however, the SNP wanted to discuss other service area cuts which were included in the Labour budget. The Conservative group agreed that the £6.045m of additional funding from the Scottish Government should be used to fight coronavirus throughout North Lanarkshire and we were disappointed at the negative reaction of the SNP group, given how serious this situation is.
“The full council meeting is scheduled to go ahead tomorrow and members of the Conservative group will be present. However, we feel that in a time of crisis, political groups should be working together, instead of arguing over how we allocate the additional funds.”
Neil McGrory - Local Democracy Reporting Service