.Council leader Denise Jeffery and leader of the Conservative opposition, Nadeem Ahmed, say they're putting their political differences aside and hope others will follow.
The pair say they are focusing their joint efforts on supporting local food banks, many of whom have been stretched by the pandemic.
The council says its buying and supplying food to local banks where their stock is low and is encouraging others to donate items where they can.
Labour's Councillor Jeffery, who took over the council in December, said: "This is not a time for politics.
"Coun Ahmed and I are very clear that we will work together on behalf of our local communities in this difficult time. We are breaking the political divide to make sure that vulnerable people are receiving the help and support that they need.
"I am very pleased to pull together on this and work as one council for everyone in this district. We will not play politics with the response to this crisis and I hope others will follow this way of working."
Coun Ahmed added: "This is absolutely the right time to work together. Coun Jeffery and I are in agreement that we can work together, in true Yorkshire spirit, to provide a safety net for anyone who may need it.
"I am very pleased to be part of the council’s response and urge everyone to put aside the politics and support the council’s response to help our residents."
With elderly and isolated residents being prioritised, the local authority also says its liaising closely with Age UK, Carers Wakefield and NOVA.
Residents are told they can donate to food banks at collections available in many local supermarkets, or at St Catherine’s Church in Agbrigg which will distribute items to food banks across the district.
Local Democracy Reporting Service