A mass Covid-19 vaccination programme will need the full support of the executive in order to be delivered, the Ulster Unionist Party leader has said.
Steve Aiken urged the first and deputy first ministers to present a united front on the importance of the vaccine.
Mr Aiken said Northern Ireland was moving to "a critical stage" of the pandemic.
On Sunday, the Department of Health reported three more coronavirus-related deaths and 351 new cases in NI.
It brings the department's overall death toll, which is based on deaths from any cause within 28 days of a positive test, to 986.
Speaking on BBC One's Sunday Politics Mr Aiken said: "All of the executive should be working together and getting the same message out.
"Now is not the time for backbiting but what we must be doing is supporting [Robin Swann] because we must support our health service to get through this stage."
Mr Aiken said he would "love" the first and deputy first ministers to "keep coherent with the message they have come out with in the past week", saying "they must do that because we're moving to a critical stage" of the pandemic.
Speaking about the vaccines, Mr Aiken said: "I really do hope that the various vaccines, their efficacy will be proved and they will be given the approval for their rollout to start."
He called on Stormont to focus on helping the economy to recover and dealing with the pandemic in the new year.
"We need to be doing this to be able to make sure we can come out the other side and make sure our health service isn't overwhelmed," he said.
The UUP leader added that the "most important thing" for the people of Northern Ireland to doing was to support the health minister.
On Saturday, the Department of Health reported nine more coronavirus-related deaths and 315 new cases of the virus in Northern Ireland.
It brings the department's overall death toll, which is based on deaths from any cause within 28 days of a positive test - to 983.
Meanwhile, it emerged that GPs in Northern Ireland are planning to deliver Covid-19 vaccines for people aged over 80 who do not live in care homes from 4 January.
Doctors have been advised to "assume" the GP vaccination programme will begin on that date.
Approval is anticipated for two vaccines in the coming weeks.
The JCVI (Joint Committee on Vaccination and Immunisation) group will decide on who should be first in line to receive it, but it has been widely reported that care home residents and health and social care workers will be the first priority groups.
GPs will be central to the programme's roll-out, with Northern Ireland relying on them along with health trusts to "urgently" begin administering the doses once the drugs are licensed, according to a letter from the Health and Social Care Board sent to GP practices.
The initiative is a "major undertaking" by GP practices to "help bring the pandemic under control" according to the head of general medical services at the HSCB, Dr Margaret O'Brien.
"Whilst clarity is still required on a number of issues, including the date of approval and delivery of the vaccine, the exact storage requirements and priority groups, the situation is developing at pace and there is a need to plan for the earliest possible commencement of the vaccination programme," said Dr O'Brien.
"We do however have enough information to be able to start to plan for a Covid-19 vaccination programme."
"This is the light at the end of the tunnel that so many of us have been waiting for," said Dr Alan Stout, chair of the GP committee at the British Medical Association.
Dr Stout said the intention is "to get started this side of Christmas" but acknowledged the rollout will be "massively challenging".
Health and social care frontline workers are expected to be vaccinated in the first phase, followed by residents and staff of care homes and the clinically vulnerable.
Without regulatory approval, plans for vaccine delivery are at this stage provisional.
The vaccination programme will be on a phased basis, and will run well into 2021, according to the Department of Health.
Plans include a public information campaign to encourage take up among the public.