It comes after the group, also known as Doctors Without Borders was ordered off the island in October, ending its service for refugees and Nauruans.
Last week it started a free service involving psychological consultations with doctors in Australia via video or phone.
Christine Rufener, a psychiatrist with Médecins Sans Frontières, said since October former patients have described worsening health conditions in Nauru.
"We continued to hear messages from the island, saying that things are worse, that they were unable to access care, that they were waiting for 3-4 weeks between appointments and we just find that unacceptable. We know our former patients are suffering, we made an ethical obligation to support them and so we want to follow through on that obligation."
Before being forced to leave, MSF provided mental health care to 285 patients, most of whom were refugees or asylum seekers.
A December report by the group found that among the 208 refugees and asylum seekers treated by MSF, 124 had suicidal thoughts and 63 had attempted suicide.
Dr O'Connor said MSF had informed the Nauru Minister of Health of its plans to establish a telehealth service but had not heard back.
She said a team of psychologists with experience in telehealth had been hired in Australia and would meet with former patients in the coming weeks.
MSF would look at expanding the telehealth services to new patients in Nauru, including local residents, after it had established services with former patients.