Labour politicians in Llanelli have attacked a decision to temporarily cut back overnight cover at a minor injuries unit (MIU).
The town's Member of the Senedd (MS), Lee Waters, called on his party leader Eluned Morgan to intervene in the decision at Prince Philip Hospital.
Llanelli's Labour mayor and the MP for the area have also raised concerns over the closure.
The first minister told the Senedd that the Hywel Dda health board had failed to recruit qualified doctors to support the unit.
The MIU will be closed from 8pm to 8am for six months from 1 November, under a decision taken by the health board last week.
The board heard the reason for the overnight closure was "due to a significant and continued lack of medical cover", which had led to concerns about the safety of patients and staff welfare.
The board also agreed to cut capacity at a children's ward in Aberystwyth's Bronglais hospital, and to close the remaining nine beds at Tregaron hospital in Ceredigion.
The Welsh Parliament heard that a protest camp has been set up outside the hospital.
In the Senedd, Lee Waters said the health board had promised that overnight care would be maintained.
"At very short notice and with no consultation or engagement they have changed their mind now."
He said staff at the health board had not been making an active effort to recruit GPs and it was "poor management of the unit that is putting people off".
Calling for the Welsh government to step in, he said: "If overnight police or fire cover was removed from one of Wales' largest towns I'd expect intervention. I don't see why healthcare should be any different."
"The health board clearly don't understand Llanelli if they think that people will just let this go."
Morgan told Waters that she "absolutely" understood "the frustration".
"The health board has attempted, as I understand it, to recruit qualified doctors to support the unit but has been unsuccessful".
This meant the unit had become nurse-led. Between February and July there were 42 uncovered slots in the rota, the Senedd heard.
Morgan said the health board had to ensure services were safe, but that it was important they listen to the local population.
The first minister added that 32% of overnight activity came from people with serious conditions "who shouldn't actually be presenting to a minor injuries unit".
"The stress of people turning up with major issues is causing a significant number of absences. I do think we have to be practical and realistic about the situation."
'People are up in arms'
Nia Griffith, the Labour MP for Llanelli, said on social media network X she was "very concerned" at the proposals at the MIU.
On the day of the board meeting she said she had asked the board why the decision was taken before a consultation, and had asked for more to be done to keep the unit "permanently open 24/7".
Llanelli town mayor, Labour councillor John Prosser, has written to Wales' health minister calling on him to intervene.
Mr Prosser wrote the letter as secretary of Save Our Services Prince Philip Action Network (SOSPPAN), a campaign group he told BBC Wales was "apolitical".
"People in Llanelli are up in arms," said the mayor, who said he stayed overnight at the protest camp.
"Staff are very supportive. Nobody wants to see it close down, because if they close it at night it will never be re-opened, we just don't believe them."
In the Senedd on Tuesday Cefin Campbell, Plaid Cymru MS for Mid and West Wales, said the alternative to the MIU is travelling to Glangwili in Carmarthenshire, or Morriston in Swansea, "both already facing huge pressures and demands on their services".
"A failure to recruit more doctors, poor workforce planning, shrinking budgets, these are the Welsh government’s failings. But, ultimately, it’s the people of Llanelli and the surrounding area who are paying the price," he said.
The first minister replied that health service funding had increased by 4%, compared with 1% increase in England.
Hywel Dda University Health Board has been asked for comment.