A community councillor said he regretted the wording of a tweet in which he said people from big cities in England were welcome because Wales had the space for social distancing.
In the tweet, Martin O’Neill said he would, in the same circumstances, do the same for his family.
The Mumbles community councillor posted the tweet on March 22 – a day before the current lockdown measures, including travel restrictions, were announced by Prime Minister Boris Johnson.
Mr O’Neill said he removed it from his Twitter account on March 22.
“I deleted it almost straight away,” he said. “I regret it, to be honest.”
He said the tweet aimed to convey his empathy for families living in cramped conditions in cities.
“I’ve got children of my own – if this was happening when they were young and we were living in a flat in a city, we would be bouncing off the walls,” said Mr O’Neill.
“People in flats are piling into parks. It’s difficult for them to do social distancing.”
Mr O’Neill said he fully supported the current restrictions requiring people to stay at home, except for going out to buy essential supplies, one form of exercise, to help someone vulnerable, and work if it was not possible to work from home.
The Labour councillor, who represents West Cross, said he had elderly relatives of his own, and had a colleague who had tested positive for coronavirus.
“These are very unsettling times,” he said.
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Like many people Mr O’Neill, who lectures postgraduates at Cardiff University’s School of Medicine, is working remotely from home.
He and fellow community councillors in Mumbles are coordinating a volunteer response team to do things like shopping and other deliveries for those in need.
Former Swansea councillor and Lord Mayor of Swansea, Ioan Richard, said he felt Mr O’Neill should be asked to resign because of the tweet.
Lord Davies of Gower and former Gower MP, Byron Davies, described the tweet as “very irresponsible and worthy of a resignation I’d have thought”.
Mr O’Neill said people had seized on it, but added that he would continue in his role.
“The criticism I’m getting for that tweet is valid – then again it’s valid in hindsight,” he said.