Martin and his coalition government partners, deputy prime minister Leo Varadkar and cabinet minister Eamon Ryan, "have agreed that the Dail (parliament) should be recalled", a spokesman said.
The news came after two days of political turmoil following revelations that a number of lawmakers and senior politicians attended a gala dinner in breach of coronavirus guidelines.
The Irish Examiner newspaper revealed 82 high profile figures, including EU trade commissioner Phil Hogan, a cabinet minister and a supreme court judge, attended the Oireachtas (parliament) Golf Society dinner on Wednesday night.
The event was held just 24 hours after the government announced fresh COVID-19 restrictions to curb a new surge in cases, including no "formal or informal events or parties" to be held at hotel restaurants.
It was reported that attendees at the dinner sat at tables of ten in breach of coronavirus guidelines, and organisers erected a room divider in a bid to skirt legislation banning gatherings of more than 50.
But police on Friday said they had opened an investigation into the event for alleged breaches of that same legislation.
Martin, the head of Fine Gael, the party for which Hogan previously served as a lawmaker, said on Saturday they had "asked him to consider his position".
A spokesman for Hogan told state broadcaster RTE on Saturday he would "reflect on" the request.
Irish agriculture minister Dara Calleary and deputy chair of the parliament's upper chamber Jerry Buttimer have both already resigned for their attendance at the event.
Ireland has reported 1,777 deaths from Covid-19 since the beginning of the pandemic and has registered nearly 28,000 infections.
Yellow vests
Meanwhile, Irish "yellow vest" activists protested against the government's Covid-19 measures in Dublin on Saturday.
The rally was organised by the Yellow Vests Ireland group - which was inspired by the larger French yellow vest movement - at Custom House Quay.
According to RTE, there was "little sign of physical distancing and most of those in attendance did not wear face coverings."
Speakers at the Yellow Vests' rally denounced the current Covid-19 restrictions and described them as unconstitutional and unnecessary.
One speaker claimed there was no evidence that wearing face coverings protect people from coronavirus.
There have been similar demonstrations against government restrictions and in particular compulsory mask-wearing organised in the UK, the United States, Germany, Spain and France.
