Ireland on Thursday scrambled to assemble potential candidates to succeed EU trade commissioner Phil Hogan after his resignation for breaching coronavirus guidelines.
Hogan, one of the bloc's most senior officials and a powerful force in Brexit talks, quit on Wednesday after a week-long stream of revelations caused rising public anger.
European Commission executive vice-president Valdis Dombrovskis of Latvia has stepped up to take over temporarily.
Her spokesman said she wanted a replacement "rapidly".
Von der Leyen meanwhile issued a stern warning to other commissioners to comply with Covid-19 rules.
As "Europeans make sacrifices and accept painful restrictions, I expect the members... to be particularly vigilant about compliance with applicable national or regional rules or recommendations", she said in a statement.
- Rumoured replacements -
Martin told Ireland's state broadcaster RTE on Thursday that he would meet his government coalition partners to discuss Hogan's replacement.
He refused to be drawn on specific names, even as rumours swirled linking past prime ministers, current cabinet ministers and European parliamentary officials to the job.
But he added: "It's fair to say that at this stage our shared objective will be that a person of very, very high calibre will be nominated by the Irish government."
Yet there is no guarantee Ireland will retain the trade portfolio, which is regarded as a key asset protecting the Republic's interests during Brexit trade talks with Britain.
Among those touted in the Irish media as potential successors are former prime minister Leo Varadkar, Foreign Minister Simon Coveney and Finance Minister Paschal Donohoe.
But all three hold key positions in Martin's two-months-old coalition government, and Donohoe was recently appointed head of the eurozone group of finance ministers.
Martin is also considered unlikely to want to weaken his administration, which has already been hit by a series of resignations and is facing a surge in coronavirus cases.
RTE raised European Parliament vice-president Mairead McGuinness and former deputy prime minister turned MEP Frances Fitzgerald as possible replacements for Hogan.
They were seen as figures who would not destabilise the coalition by prompting an unwelcome by-election.
Other names said to be in the frame include the former EU ambassador to the United States, David O'Sullivan, and former prime minister Enda Kenny.
The Irish Times, citing party sources, speculated candidates will come from the centre-right Fine Gael party Hogan served as an Irish lawmaker under the terms of the coalition deal.
It is thought the government may have already had a plan to replace Hogan -- a former Irish government minister and EU agriculture commissioner -- after he made a failed run for the head of the World Trade Organization in June.
- Covid-19 breaches -
On Wednesday the Irish government said 60-year-old Hogan's resignation was "the correct course of action".
Martin piled pressure on Hogan to quit after it emerged he travelled through a county in a local lockdown and flouted guidelines for a 14-day quarantine on arrival in Ireland.
Hogan also attended a parliamentary golf club dinner on August 19 in breach of coronavirus restrictions on social gatherings announced just 24 hours earlier.
The sporting evening was attended by around 80 people -- including a cabinet minister, a supreme court judge and lawmakers from Ireland's upper and lower houses of parliament.
It is being investigated by police under legislation limiting gatherings to 50 and has prompted a series of high-level resignations, including agriculture minister Dara Calleary and deputy Senate chair Jerry Buttimer.
Hogan initially declined to apologise for his attendance at the event and details of his travels across Ireland emerged fitfully.
Embarrassment was compounded when it was revealed he was pulled over by an Irish police officer for using his phone while driving.
"I deeply regret that my trip to Ireland ... caused such concern, unease and upset," Hogan said in his resignation statement.AFP