The PUP has also reported the matter to the police to investigate "potential incitement and criminal damage".
But not everyone at Stormont was unhappy.
"Looking forward to going back to Stormont tomorrow! #flytheflag," Sinn Fein MLA Raymond McCartney wrote on Twitter.
Sinn Fein MEP Martina Anderson wrote: "Irish flag flown over Stormont - whether authorised or not it is right that the Irish flag should fly over Stormont and other buildings too."
DUP MLA and Assembly chief whip Peter Weir has written to Assembly Speaker Mitchel McLaughlin and chief executive Trevor Reaney "demanding an explanation" as to why the flag went up yesterday.
The roof and the fourth floor of Parliament Buildings are currently undergoing building work.
Mr Weir added: "Whatever the motivation behind this, there must be a full explanation from the Assembly as to who had access to the flagpoles and who was responsible for this action.
"If it was carried out by someone working for an outside contractor then this surely would represent a breach of contract, which should result in sanction.
"It would also place an onus on the company to take disciplinary action against those responsible.
"I have inquired too whether the Union flags, flying to mark Coronation Day, were interfered with yesterday (Tuesday).
"I have been assured by the Assembly that these were rogue actions and are being fully investigated."
Winston Irvine of the PUP shared the photo on Twitter and said he had reported the incident to the PSNI.
Mr Irvine said if someone removed the "stars and stripes from the White House it wouldn't be taken that lightly", and said it was an issue of "potential incitement and criminal damage".
"We certainly believe a crime has been committed and the law has been broken and the police are carrying out a full and thorough official investigation," he said.
Fermanagh and South Tyrone UUP MP Tom Elliott said the brief flying of "two republican flags" would provoke community tensions.
"It was no doubt done to attract attention and cause offence and annoyance," he said.
"The Ulster Unionist Party will be seeking a full explanation of how this could happen.
"We are perfectly clear that the Union flag is the only flag that should fly over Stormont in order to reflect and respect the sovereignty of the United Kingdom."
Traditional Unionist Voice leader Jim Allister called it "a serious breach of protocol and absolutely unacceptable".
A PSNI spokesman said: "We are aware of the flag and are investigating the circumstances."
The Assembly Commission - which is responsible for hoisting the flag - is also investigating.
A spokesman said: "The Speaker is clear that the commission needs to be able to consider this matter in full possession of the facts of the situation."
Mr McLaughlin has invited members of the commission to a briefing today for an update from the Assembly Clerk on any initial findings about the incident.
"A full meeting of the commission will then be held on Monday when all commission members are available and when it is anticipated that more information will be known," the spokesman added.
“The Northern Ireland Assembly was made aware that two flags were flown without permission from the roof of Parliament Buildings for a short time today. As soon as the Assembly was made aware of the incident, the flags were removed. The Assembly is investigating the incident.”
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