CORRECTED-Qatar Airways expects to re-open routes this month

(Corrects number of destinations flown to, in third paragraph)

* Anticipates countries to ease air travel restrictions

* Targets 52 destinations in May, 80 by June

* Demand for short-haul flights to rebound first

DUBAI, May 6 (Reuters) - Qatar Airways said on Wednesday it would this month start to rebuild its network, in anticipation countries will ease air travel restrictions and based on monitoring of passenger trends.

State-owned Qatar Airways has been one of few airlines to continue regular, scheduled flights during the global lockdowns to contain the novel coronavirus, maintaining services to around 30 destinations.

It will gradually resume flights to some of the 165 destinations it served before the outbreak, aiming to fly to 52 destinations by the end of May and up to 80 destinations in June.

"We have built a strong level of trust with passengers, governments, trade and airports as a reliable partner during this crisis and we intend to continue delivering on this mission as we gradually expand our network," Chief Executive Akbar al-Baker said a statement.

But the airline said entry restrictions were constantly evolving, making it difficult to predict future travel.

Short-haul travel was expected to recover first, while demand between large global cities will take time to pick up, even though people will want to see friends and family after months of lockdown.

Flights would be added gradually, the airline said, based on monitoring passenger flows and booking trends.

By June, it aims to fly to 33 Asia-Pacific destinations, 23 across Europe, 20 in the Middle East and Africa and four in the Americas, many of which have banned foreigners from entering.

The aviation industry has been among the hardest hit by the coronavirus crisis, which has destroyed travel demand as governments closed their borders.

Qatar Airways in March said it was burning cash reserves and would eventually seek government aid. It has since temporarily cut salaries and told staff to prepare for substantial job cuts.

Gulf rival Etihad Airways planned to start resuming passenger flights in May, only to later delay until mid-June. (Reporting by Alexander Cornwell; editing by Louise Heavens, Elaine Hardcastle and Barbara Lewis)