The Irish Medical Organisation has said it will consider an invitation from the Labour Relations Commission to return to talks when its junior doctor committee meets tomorrow.
The committee will also discuss the next stage of industrial action to be planned for next week, should the HSE fail to agree meaningful sanctions for failing to reduce excessive hours.
The invitation from the LRC followed a letter to the IMO from the Health Service Executive which accepted the need for financial sanctions to prevent NCHDs being forced to work dangerous hours.
Earlier, Minister for Health James Reilly said less than half of the original estimated 15,000 patients were affected by the strike action.
Around 3,000 non-consultant hospital doctors took part in the day-long action in protest over working hours, which the IMO said are in breach of the European Working Time Directive.
Mr Reilly said the impact on services was considerable but not half as bad as people had predicted.
He said around 6,000 patients were affected and this was painful for them.
The minister appealed to the IMO and junior doctors to "go back to the LRC" to resolve the dispute.
Speaking in the Dáil, Mr Reilly said the Government was keen to see the matter resolved.
The IMO said its members did not take the action lightly but were determined to see their campaign through.
It said it has had exceptional support from the public, other health staff and other doctor for its strike.
IMO Assistant Director of Industrial Relations Eric Young said he hoped the action brought home to the HSE that there is no support for their position.
He said the IMO would consider how to escalate the dispute in the absence of progress with the HSE, but would continue to try to minimise the impact on patients.
Mr Reilly said those people who had appointments cancelled would have them rescheduled and go to the top of the queue and have their operations as soon as possible.
Emergency services, oncology, and other key services functioned throughout today's action at 51 hospitals around the country.
Under Medical Council guidelines doctors may withdraw services, but cannot be released from their ethical responsibilities to provide emergency services.
Public hospitals operated a service that would normally be provided on a Sunday.
Mr Reilly said that now that the IMO had held a one-day strike, they should come back to the table and talk.
He said managers would be relieved of their command if they failed to implement the reduced working hours as planned.
However, he added that financial sanctions should not be imposed on hospitals as that would hurt patients.
Chairman of the NCHD committee of the IMO Dr John Donnellan said the HSE was responsible for the withdrawal of services.
"They have misled doctors, they have broken promises and commitments and they have ignored their obligations under EU law.
"Enough is enough. We are not taking this anymore."
The Irish Nurses and Midwives Organisation said its members have been advised not to undertake the duties of NCHDs.
Speaking on RTÉ's Morning Ireland, General Secretary Liam Doran said nurses supported the doctors' dispute.
"We're solid with our doctor colleagues as they strive to have something implemented which should have been implemented nine years ago," he said.
Agreement has not been reached between the IMO and the Health Service Executive despite lengthy talks at the Labour Relations Commission and a set of proposals from HSE management.
Concern for patients
The Irish Patients' Association called for patients affected by today's action to be made priority cases.
Chief Executive Stephen McMahon said: "We don’t want the patients affected today to become emergencies."
Mr McMahon said the association understood that procedures in private hospitals would not be affected by the strike.
"Outpatients appointments and elective surgeries (in private hospitals) will not be affected by this dispute because it seems they have their roster sorted out," he said.
The patients' association said it supported the doctors' cause, but objected to the "means to reach that end".
Meanwhile, a cardiologist and professor at the Conway Institute at UCD said today's strike by non-consultant hospital doctors is "morally reprehensible" and misguided.
Professor Eoin O' Brien told RTÉ News that refusing to treat a sick patient goes against everything a doctor is trained to uphold.
He said the strike was misguided and he called on junior doctors to look at alternative forms of industrial protest rather than denying sick people the treatment they need.
An alternative he said would be to refuse to participate in all HSE administrative functions, such as sitting on hospital committees, and a refusal to sign certificates such as sick and death certs.
Prof O'Brien said no one can estimate how many of the 12,000 patients whose outpatient appointments have been cancelled and the 3,000 patients whose planned operations were cancelled will suffer what may be a fatal outcome by not having their illness treated at a curative stage.