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Tony Abbott says the families of those lost in Malaysia Airlines flight MH 370 will be welcomed to Australia if they wish to visit and their visa fees will be waived.

The prime minister has offered his condolences to loved ones of passengers on the doomed flight that is now believed to have crashed in the Indian Ocean off Western Australia.

“This has been a desperately difficult time for thousands and thousands of people right around the globe, particularly in China as well as in Malaysia,” Mr Abbott told reporters.

“I understand that the loved ones of those on that plane may well wish to come to Australia in the coming days and weeks.

“They will find a welcoming country that is more than willing to embrace them in this very difficult time.”

I want them all to know that should they come here, they will be in the arms of a decent country.

Mr Abbott spoke to the Malaysian prime minister on Tuesday morning to offer Australia’s continuing support and cooperation.

Mr Abbott says the search mission has now become one of recovery and investigation.

“It’s a long way from anywhere but obviously it’s closer to Australia than anywhere else and Australia has much of the capacity needed to get this done as best it can be,” he said.

Mr Abbott told parliament the visa fees of the bereaved families would be waived, adding a formal condolence motion would be moved on Wednesday.

“I want them all to know that should they come here, they will be in the arms of a decent country,” he said.

Opposition Leader Bill Shorten also offered his support to the families of those lost in the disaster which had “touched us all”.

He commended Australian searchers for their efforts in an extremely difficult task.

“Australia is proud of the Australian contribution and I believe the world is grateful to them,” Mr Shorten said.

“The search has brought nations together.”