Kaci Hickox maintains isolation is unnecessary, as she has no symptoms and has tested negative for Ebola.
Maine's governor is pursuing legal action to enforce her compliance.
Nearly 5,000 people have died of the disease in West Africa, but only nine patients have been treated for the virus on US soil.
More than 13,700 people have been sickened in total, the vast majority in Liberia, Sierra Leone and Guinea.
Ebola, which is only spread through close contact with the bodily fluids of a sick patient, has an incubation period of up to 21 days, during which patients neither show symptoms nor are infectious.
US officials are at odds over whether American healthcare workers who return from treating Ebola patients in West Africa should be forced into quarantine until that period has expired.
New Jersey and other states put quarantine rules into place after a New York doctor who treated Ebola patients in West Africa came down with the disease.
But the US Centers for Disease Control and Prevention (CDC), America's chief public health agency, merely recommends daily monitoring of returned health workers, rather than enforced isolation.
And President Barack Obama has warned that overly restrictive measures imposed upon returning healthcare workers could discourage them from volunteering in Africa.
"We know that the best way to protect Americans from Ebola is to stop the outbreak at its source," he said on Wednesday.
Ms Hickox returned to the US on Friday, landing at Newark International Airport.
Officials say she had a minor fever, necessitating a quarantine at a Newark, New Jersey, hospital.
Ms Hickox contested the quarantine regimen, ultimately threatening legal action.
After showing no fever or other symptoms for a 24-hour period, she was discharged and brought to her home state of Maine.
On Thursday morning, Ms Hickox left her home on a bicycle, followed by police officers who monitored her movements and public interactions. She returned home shortly after.
Without a court order, the police were barred from detaining her.
"I really hope that we can work things out amicably and continue to negotiate," she told the Associated Press news agency on Thursday morning.
Maine Governor Paul LePage's office said later that negotiations with Ms Hickox over her compliance with CDC guidelines for health workers who have had her level of exposure to Ebola had broken down, and that he would "exercise the full extent of his authority allowable by law".
"I was ready and willing - and remain ready and willing - to reasonably address the needs of healthcare workers meeting guidelines to assure the public health is protected," Mr LePage said in a statement.
The governor's office did not disclose what steps it would take to force her compliance. But it said she should refrain from going out in public save for solo exercise or walks, submit to direct monitoring, and agree to co-ordinate travel with public health authorities, among other measures.
Meanwhile, US Ambassador to the UN Samantha Power, who has recently returned from a trip to the Ebola-hit countries in West Africa, said the "lives of a whole generation in west Africa" depend on the world's ability to stop the outbreak.
"Ebola thrives on fear," Ms Power said. She said it was well known what was needed to stop the outbreak but the world needed to "marshal the will" to do it.
While "there are a few nations doing a lot to help, many are doing very little or nothing at all".
In other developments:
A UK ship has arrived in Sierra Leone carrying food, medical equipment and 32 pick-up trucks, to help keep hard-pressed Ebola treatment centres in operation
North Korea has instituted a 21-day quarantine for any foreign national arriving from any country
The World Bank said it would immediately provide $100m to fund the deployment of more health workers to West Africa.
