A meeting of the party's ruling officer committee was held earlier on Thursday.
DUP leader Gavin Robinson said the first minister's "arrogance will have consequences", but O'Neill accused the party of being "reckless and irresponsible".
"Her complaints today that she's frustrated from engaging with the British Prime Minister within the sovereign United Kingdom will so be it because her law breaking must have consequences," Robinson said.
O'Neill said the DUP leader's comments were "arrogant and supremacist" adding that the DUP "is consumed with their own internal leadership troubles and divisions".
She said she would be at the Assembly on Monday with her party colleagues to "keep showing up every day for people".
Earlier she described the move to block the meeting with the prime minister as "reckless and irresponsible" and meant people in Northern Ireland "will not be represented".
"This is a reactive stunt, driven by the DUP's own internal pressures and electoral problems," she said in a statement…