The DUP deputy chair of Stormont's finance committee has accused Sinn Fein minister Conor Murphy of having "lost the run of himself".
Paul Frew branded the Finance Minister's comments blaming lockdown on years of Tory austerity as "illogical and irrational".
Although First Minister Arlene Foster declined to become involved in the row, the remarks from a senior DUP MLA about his party's partner in government are significant.
SDLP and Ulster Unionist MLAs described Mr Murphy's comments as "bizarre" and "baffling".
The Finance Minister was at the centre of controversy in March over a joint PPE order with Dublin and over his 2007 remarks branding IRA murder victim Paul Quinn a criminal.
The Sinn Fein minister told Radio Ulster that coronavirus restrictions might not have been required if "years of Tory austerity" had not left the health service in a challenging position.
He said that if we had a "robust health service which was well resourced", it could have coped with the pandemic.
"The reason we had to go into lockdown, and people should understand this, is because the health service has been under-resourced through austerity cuts for many, many years," he added.
Amidst extensive challenges to his claim, Mr Murphy later tweeted: "Austerity policies have severely impacted on the capacity of health and social care services, here and elsewhere, to respond to the Covid 19 pandemic.
"For clarity, lockdown has been absolutely necessary to save lives."
Mr Frew said that the minister was "quite rightly" trying to backtrack and "eat his own words" on his original position.
"Conor Murphy's comments about lockdown are illogical and irrational," he stated.
"As Arlene Foster said earlier: 'Every government in the world entered lockdown to protect life'.
"It's about time that Conor Murphy learned his lesson to focus on his job rather than always trying to score a political point.
"He was so focused on getting a whack at the Tories that he lost the run of himself."
SDLP MLA and finance committee member Matthew O'Toole said: "These bizarre and inexplicable remarks don't inspire confidence, especially when the department is still failing to explain a phantom PPE order that was promised, never delivered, and apparently never existed.
"The Finance Minister should correct his comments. Public messaging during a health crisis is important and, on this occasion, it seems to have gone wrong again."
Mr O'Toole said that Tory austerity had placed the health service under immense pressure.
But there was "no evidence" that "the reason for the Covid-19 lockdown" was due to under-funding.
The South Belfast MLA said: "Other developed economies, which spend a higher proportion of GDP on health services, have also entered lockdown to prevent onward transmission of the virus and save lives.
"It's baffling, therefore, that the minister in charge of financing our response to the Covid-19 pandemic seems to have a view at odds with most other countries in Europe and the scientific community."
Ulster Unionist MLA Alan Chambers said that the Sinn Fein minister's claim was "utterly without foundation and completely incompatible with reality". He said: "Conor Murphy's feeble attempt at providing 'clarification' about his incoherent comments on lockdown, via a tweet, makes the situation worse because he singularly fails to explain why he said what he said in trying to blame the UK Government for lockdown.
"He has failed to retract the comments he made. Attempting to blame 'the Brits' for lockdown is pathetic.
"For a party that has had so much to say about the response to Covid-19, I would have expected Sinn Fein to have a much better grasp of the situation."
Mr Chambers said that even with "maximum funding for the health service", Northern Ireland would still have needed lockdown to limit the spread of coronavirus and save lives.
He added: "Countries across Europe, and indeed the world, were implementing lockdown.
"Conor Murphy's own party leader said that we should be following the World Health Organisation's advice on lockdown, so his failure to retract his original comments run directly counter to what they were saying."
TUV leader Jim Allister said: "Sinn Fein was the chief cheerleader for lockdown, agitating for more and urging anger in response to delay.
"Everyone knows lockdown was to stop the spread of the virus - clearly Murphy thinks he knew better than the medical advice his Executive was receiving."
UUP Health Minister Robin Swann told Radio Ulster: "It wasn't because our health service wasn't fit to cope. No health service was fit to cope with what we saw."