Health Minister Michael McGimpsey has asked the Northern Health Trust to look into the possibility of extending the opening hours for the Mid Ulster Hospital's minor injuries unit.
The hospital's accident and emergency department was closed earlier this month.
It was downgraded to a minor injury unit due to safety concerns.
Vice Chair of the Health Committee Sinn Fein MLA Michelle O'Neill said she would support longer opening hours.
"If they were available at weekends and evenings, I think that's something that the community would very much welcome.
"It's something that I want to pursue further with the trust and with the staff who work on the hospital site."
On Friday, the SDLP's Patsy McGlone said that "mooted calls for extended opening times" at the unit "is not enough to properly serve the health needs of the local people".
He said that they "can only be properly served with the re-introduction of accident and emergency services to the Mid Ulster Hospital".