O’Neill and other senior Sinn Féin figures have been interviewed by police investigating last month’s unnotified demonstrations in Portadown, with unionists accusing the party of acting unlawfully.
The Sinn Féin deputy leader has defended her involvement, saying it was the “right thing to do”.
The Traditional Unionist Voice (TUV) leader Jim Allister said “the DUP’s sham response today was beyond pathetic” adding “the DUP is interested only in clinging to office, not principle”.
Alliance leader Naomi Long said refusing to attend or preventing others from attending the meeting with the prime minister was reckless and put party interests ahead of Northern Ireland’s economic future and the needs of the public.
The Ulster Unionist Party leader Jon Burrows told BBC’s Evening Extra programme the situation was a “political fudge” that was “all choreography and no consequences,” adding that the move would “probably galvanise Sinn Féin further at the ballot box.”
The Social Democratic and Labour Party’s (SDLP) Matthew O’Toole said “plunging this place into more political chaos is not a sensible strategic move for unionism”.
“Ultimately it’s only going to make reasonable people here conclude that the largest unionist party simply doesn’t want to make the status quo work,” he added.
The DUP has been under pressure from unionist rivals and some within its own ranks over how to respond to the row over Drumcree.
Last week, DUP MP Carla Lockhart stepped down from the party’s officer board over their leader Gavin Robinson not withdrawing Little-Pengelly to force O’Neill from their joint Stormont office.
On Thursday Lockhart said she will follow her “own course” if the party does not seek to remove Sinn Féin’s Michelle O’Neill as Stormont’s first minister.
Robinson said that while O’Neill and her party colleagues “should be punished, that does not include punishing the rest of Northern Ireland”.
The Upper Bann MP, who last week quit the DUP’s ruling officer board in opposition to party leader Gavin Robinson’s approach, outlined her position in a letter to colleagues which she later posted on Facebook.
Other DUP representatives including assembly member Diane Forsythe have since backed Lockhart’s calls for O’Neill to be “removed from office”.
On Tuesday, Forsythe said that in the absence of such “meaningful action”, official engagements through the joint Executive Office should be stopped immediately as a “bare minimum”.
On Wednesday, a second DUP assembly member called for O’Neill to go.
Maurice Bradley said removing O’Neill “would not, in itself, require the Assembly to collapse”.
