SDLP leader Colum Eastwood has called on the Prime Minister to sack Dominic Cummings and prove that "the privileged Tory elite" are not unaccountable.
And Alliance deputy leader Stephen Farry said the actions of Boris Johnson and his special adviser conveyed "a sense of entitlement and hypocrisy".
People Before Profit MLA Gerry Carroll said that Mr Cummings was putting compliance with the continuing lockdown at risk and he must "step down or be kicked out".
The SDLP and Alliance will hold a virtual meeting with Labour, the SNP, and other Opposition parties at Westminster on Tuesday to "discuss the next steps in holding Boris Johnson and Dominic Cummings to account."
Sinn Fein, the DUP, and Ulster Unionists did not respond to requests for comment.
Mr Cummings on Monday expressed no regret for driving 264 miles during the lockdown. He refused to apologise and insisted he had behaved "reasonably and legally".
Mr Eastwood said: "Dominic Cummings' behaviour has critically undermined the British Government's public health messaging during this crisis.
"For all the confusion in their approach, the 'Stay at Home' message was not complex. No-one could reasonably interpret that as giving a green light to travelling hundreds of miles to Durham and then travelling further to a beauty spot to test your eyesight.
"This is now a test of this Conservative government. They have a simple question to answer - what is more important, saving Dominic Cummings' job or saving lives? There is only one answer.
"This crisis is continuing to claim lives. People need to know that the sacrifices we're all making - being separated from family and friends in traumatic circumstances - is not in vain.
"They need to know that the privileged Tory elite are not immune from accountability or the rule of law."
Mr Carroll said: "Dominic Cummings has shown the typical arrogant, elitist attitude that you'd expect from a Tory adviser.
"This government has been disastrous throughout the coronavirus crisis. Cummings' behaviour reflects contempt for the challenges faced by ordinary people during lockdown.
"He thinks the rules should not apply to him. It's time that he stepped down or was kicked out.
"His breaches of public health guidelines have put lockdown at risk. There is an increasing chance that more people will now disregard it."
Dr Farry said he had seen a huge surge in emails from constituents expressing outrage at Mr Cummings' actions and Mr Johnson's support for him.
The North Down MP said: "The actions of the two men speak of a sense of entitlement and hypocrisy.
"They stand in sharp contrast to almost everyone else following the regulations and guidance, and who have often made considerable personal and family sacrifices."
The Alliance deputy leader said Mr Cummings' own words showed that he had driven "a coach and horses" through lockdown guidelines.
"The coherence of the remaining aspects of the lockdown are now in serious jeopardy," he said.
"This episode further undermines good governance, accountability and public trust. Questions aren't going away and pressure for the removal of Mr Cummings from public office will continue from Alliance and other parties."