A mental health trust under pressure amid safety concerns has claimed a public inquiry would compromise current care.
Earlier this week, the chairman of the Norfolk Health Overview & Scrutiny Committee, wrote to the health secretary calling for a public inquiry.
He said there were “enduring” safety concerns at the Norfolk & Suffolk NHS Foundation Trust (NSFT).
The trust has written to the government saying an inquiry would "compromise services" and efforts to improve.
A Department of Health and Social Care (DHSC) spokesperson said the safety and care of mental health patients "is of paramount importance".
"That’s why the Health Services Safety Investigations Body (HSSIB) is taking forward a national investigation into mental health inpatient settings," they added.
The findings will "identify risks" that can be addressed.
Last year, an independent report by the audit firm Grant Thornton found that NSFT had lost track of figures for patient deaths.
NSFT has said an inquiry would affect current services.
The trust has faced renewed scrutiny after it emerged Bartlomiej Kuczynski, who is believed to have killed his two daughters and sister-in-law before killing himself at Costessey, near Norwich, had been a patient.
The trust has announced a serious incident review into his care would take place.
Public inquiries are major external investigations that provide legal powers to compel witnesses to testify and release other forms of evidence.
Families and campaigners are among those supporting calls for one.
Natalie McLellan, whose daughter Rebecca died in Ipswich while under the care of NSFT, has joined those calls.
"We found out that there is a catalogue of disaster in Norfolk and Suffolk," she said.
"What is happening out there is not working.
"The only thing that is going to change that is a public inquiry and the only people that can ask for that are the family that it means something to.
"Rebecca has just become a name to them, but she meant everything to us."
A spokesperson for NSFT and two NHS integrated care boards covering Norfolk and Suffolk said they wrote to the secretary of state for health on Thursday to express concerns about the scrutiny committee's letter.
They said: “Although we have deep sympathy for everyone who has lost a loved one, we know that unfortunately, any public inquiry into events covering a decade or more requires an enormous amount of time and energy from current leaders and staff, inevitably compromising the services provided today and the continuing efforts to improve them."
The trust and its partners said they asked for the secretary to consider the "pace, growing strength and focus of the partnership working between both ICBs and NSFT" for changes needed in mental heath services.