The two women left the tour bus in the town of Salalah when they were fatally struck by a car on Thursday morning (September 27) at around 11am.
A male passenger was also seriously injured in the incident and was taken to hospital where he is now in a stable condition.
All three passengers, who were travelling in Boudicca, are British. The party were en route to Souq Al Haffa when the collision happened.
“Our deepest sympathies are with the families and loved ones at this very tragic time,” said the line in a statement.
Investigations into the crash are ongoing. The passengers’ families have been informed and arrangements are being made to reunite them with their loved ones.
Boudicca is currently sailing a 14-night Authentic Arabia fly-cruise, which left Aqaba in Jordan on September 20.
“The safety of all guests and crew is Fred. Olsen’s utmost priority,” the line added.
“We continue to work closely with the local tour operator, the authorities in Salalah and Oman and the UK Foreign and Commonwealth Office to provide full support to all those affected.
“A crew member from Boudicca has remained behind in hospital with the injured guest, and a senior member of Fred. Olsen’s UK head office team has flown to Salalah to provide additional assistance.”
A Foreign Office spokesperson confirmed it was supporting the families of two British nationals concerned in the crash.