Political rivals have urged the North Antrim representative to resign after allegations he holidayed in the Maldives courtesy of the Indian Ocean nation's government.
The DUP has pledged to examine the "very serious" claims levelled in a BBC Spotlight NI investigation.
Mr Paisley has denied the holiday was paid for by the Maldives government, instead insisting an unnamed friend part-funded the 2016 vacation.
Sinn Fein, the SDLP and Ulster Unionists have written to the Parliamentary Commissioner for Standards Kathryn Stone urging her to investigate the case.
Mr Paisley himself contacted Ms Stone's office on Wednesday to seek a meeting to discuss the claims made.
Sinn Fein and the SDLP said Mr Paisley should resign and, if he did not, DUP leader Arlene Foster was obliged to take action against him.
Traditional Unionist Voice leader Jim Allister said the programme raised serious questions over his rival's judgment.
The claims aired by Spotlight came days after Mr Paisley returned to Parliament having served a 30-day suspension for failing to declare two holidays paid for by the Sri Lankan government and lobbying on its behalf.
He narrowly avoided facing a by-election after Parliament's first ever recall petition fell short of the number of constituent signatures required to oust him by around 450.
Commenting on the latest claims, Sinn Fein vice president Michelle O'Neill (above) said the MP should have resigned "months ago".
"It's the latest in a long line of scandals associated with the DUP and Ian Paisley in particular," she said.
"I think Ian Paisley should have resigned many months ago and I think where he finds himself again today at the centre of another scandal is not anything befitting of someone who holds public office."
At last month's party conference in Belfast, DUP leader Mrs Foster apologised after acknowledging that standards of conduct within the party had fallen short in a number of areas.
At a press conference on Wednesday, Mrs O'Neill said: "I think that what we need to see now is more than fine words at a party conference, I think those fine words need to be acted upon and I think this will be the first test of Arlene Foster's comments at her party conference."
SDLP leader Colum Eastwood has called for Mr Paisley to quit.
"It really is time for Ian Paisley to resign," he said.
"If he doesn't, then the onus is on Arlene Foster to remove him from the DUP."
Mr Paisley denied the holiday was paid for by the authorities in the Maldives and said he is satisfied he did not need to declare the trip on the register of interests at Westminster.
The MP said he paid for part of the holiday himself, while the rest was paid for by a long-term friend who was unconnected to his work.
He declined to reveal the identity of the friend.
Mr Paisley had been suspended from the DUP pending a party investigation into the Sri Lankan controversy, but the censure was subsequently lifted.
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