Owen Mor, situated on Culmore Road, caters for people with learning disabilities and dementia.
The facility remains under enforcement after the health regulator, the RQIA, raised safety concerns in August.
An investigation in May found patients missing medicines, nurses not following procedures and inadequate record keeping.
In an unprecedented move, the RQIA obtained a court order in August to stop new admissions after it emerged the Western Trust was still referring patients to the home.
Asked if he could make any guarantees over current residents’ safety, Mr Lynch said he could not make any assurances people in the nursing home are safe under the current standards.
“How can I have the assurance that all residents in that home are safe when we have the head of older people services at the Trust saying he can’t make that guarantee”, Mr Lynch said.
“I don’t believe you can make that statement as long as the home remains in failure to comply with the minimum standards.
“How you can say you can be assured that people are safe?
“It is an unbelievable situation that six months on that this is the case”, he said.
Dr Bob Brown, the director of care and older people’s services at the Western Health Trust, told BBC Radio Foyle on Thursday: “It is not possible for me to give assurance that every resident is receiving safe and quality care at every moment in time.”
He met with councillors at a health and communities committee meeting at the Guildhall on Thursday to address concerns over the 81-bed facility.
Relatives of Owen Mor residents were in the public gallery and applauded as councillors from Derry and Strabane District Council raised their fears with the Western Trust.
One of those councillors, Raymond Barr, had his daughter admitted to the Culmore Road home last year for three weeks.
Four years ago the independent councillor’s daughter suffered a diabetic coma which left her blind and disabled.
He said he was shocked by a number of incidents during that time and said there had been a failure to give his diabetic daughter her insulin.
Asked about the current status of the Owen Mor facility, Dr Brown said: “It takes time to achieve sustainable improvement.”
In May, inspectors highlighted failings around patients missing medicines, nurses not following procedures and inadequate record keeping around falls, feeding and nutrition.
Aidan Hanna of patient advocacy group NI Patient Voice believes the care home should be closed unless serious changes are made.
“Under the current ownership I don’t believe it should be open,” he said.
A spokesperson for Owen Mor management said they have been “working closely with its regulator the RQIA and the Western Trust to move to full compliance and have the current enforcement notice lifted”.
A spokesperson for the regulatory body the RQIA said: “Owen Mor remains under enforcement action.
“During our most recent inspection in late October, we were pleased to find significant progress towards addressing the concerns identified by RQIA.
“The safety and wellbeing of everyone living at Owen Mor is of utmost importance,” the spokesperson said.