Northern Ireland's Agriculture Minister Gordon Lyons does not have the authority to halt work on new permanent border control posts (BCPs), according to Sinn Féin MP Chris Hazzard.
Mr Lyons said his action on Friday was responding to "practical difficulties" caused by the NI Protocol.
He added there was a risk NI "would not be able to cope" when grace periods end.
Mr Hazzard said the decision represented a "very foolish solo run".
The protocol is part of the UK-EU Brexit deal which keeps Northern Ireland in the EU single market for goods, thus removing the need for border checkpoints in Ireland.
However, additional checks and restrictions have been placed on Great Britain to NI trade, prompting opposition from unionists.
Grace periods, which mean the checks and controls have yet to be fully implemented, will end from April.
Existing temporary BCPs are continuing to operate.
Mr Hazzard, the MP for South Down, told the BBC's Sunday Politics programme "the executive collectively have legal responsibility around the effective implementation of the agreement and the protocol".
He said he understood the acting-DUP minister's decision had not been raised at the executive's meeting the previous day and ministers did not have "advance warning" before it was made public on Friday.
On Friday, Mr Lyons also said he had asked officials to stop recruiting BCP staff.
It is understood officials are seeking legal advice on whether or not they can follow the orders.
Previously, Agriculture Minister Edwin Poots sought legal guidance about whether he could instruct officials not to operate the BCPs, but he was advised this would be unlawful.
'Stop playing games'
In response to Mr Lyons' action, Infrastructure Minister Nichola Mallon, Finance Minister Conor Murphy and Justice Minister Naomi Long invoked a three-minister rule on Friday which called for an urgent meeting of the executive.
This has yet to take place.
On Sunday, Chris Hazzard said the DUP had "walked off the pitch" and need to "stop playing games".
The situation is "deeply, deeply regrettable", he added.