(Adds details on airline operations and background throughout)...

(Adds details on airline operations and background throughout)

July 30 (Reuters) - Airline Regional Express Holdings (REX) , which serves rural towns in Australia, has entered voluntary administration and its Boeing 737 fleet has been grounded, its administrators Ernst & Young said on Tuesday.

Rex's flights between major airports have been cancelled, E&Y said, adding that the carrier's Saab 340 twin-engine flights are currently unaffected by the voluntary administration and will continue to operate.

Rex suspended trading of its shares on Monday pending an announcement. The update comes just three months after Australian low-cost airline Bonza collapsed.

Australia's Transport Minister Catherine King said earlier in the day the government had contingency plans to ensure airline services continue in rural areas, but did not promise any bailout packages for Rex.

Rex operates in a domestic market dominated by Qantas (QAN) and Virgin Australia, which together control about 90% of Australia's airline market.

Separately, Virgin Australia said it has offered customers with existing tickets on a cancelled Rex flight to rebook on an equivalent Virgin Australia service for free.

The two companies are also exploring opportunities to support regional customers, which include Virgin Australia selling Rex's regional services through codeshare or interline arrangements, according to E&Y.