Sinn Féin councillor Barry McElduff visited some of the people moved from their homes.
“There’s kind of an atmosphere of calm at this time. I think that people are hopeful; that this alert could be lifted soon,” he told BBC News NI.
“But obviously a huge amount of inconvenience to local people in the early hours of the morning – the middle of the night effectively.
“We don’t know the nature of the alert right now, but people do not need disruption of this or any other kind.”
DUP councillor Errol Thompson condemned those responsible for the security alert.
He said Omagh had “suffered enough over many years, due to acts of terrorism”.
“This just brings back all the trauma of the past decades,” he added.
Thompson asked anyone with information to contact the police.