Relatives of passengers and crew on board Malaysia Airlines MH370 spoke of their emotional turmoil and agonising wait for news Thursday after reports emerged that a piece of the missing jet may have been found.

Aviation investigators are heading to the French, Indian Ocean island of La Reunion after a two-metre (six-foot) long piece of wreckage, which appeared to be part of a wing, was found Wednesday by people cleaning up a beach.

The discovery has raised hopes it could be from the Boeing 777 plane, which diverted from its Kuala Lumpur-to-Beijing route shortly after takeoff on March 8 last year.

No trace of the plane, which was carrying 239 passengers and crew, has been found despite a massive surface and underwater search.

Some relatives said they had mixed feelings, as they struggled with a desire for closure and hopes that those on board might still be alive.

Sara Weeks, the sister of MH370 passenger Paul Weeks of New Zealand, said she "felt a bit sick" when she first saw the reports on television.

"There's not a day I don't think about (what happened)," she told Fairfax New Zealand.

"I'm hopeful, in another respect, I'm not. I guess while you don't know, you still hope.

"We need to know what happened... at least if it's confirmed as a part of the plane then we can go onto the next stage which is still pretty similar to where we were before -- what happened, where's the rest of the plane and where's my brother."

G. Subramanian, whose Malaysian son S. Puspanathan was on board, told AFP that his heart broke every time friends and relatives asked about the 34-year-old.

"I hope we can confirm this is from MH370. I want a closure to this mystery," he said, adding: "But we hold to the belief that Puspanathan is still alive."

'We are just waiting again'

Many passengers' next of kin have criticised Malaysia's handling of the disaster and some questioned the reports of the La Reunion discovery.

"We do not want to listen again to some officials saying they are 99 percent sure. Instead we want a 100 percent confirmation," Chinese relatives said in a joint statement on the online social messaging service Wechat, urging a quick definitive answer on the source of the debris.

debris
Location of where a two-metre piece of wreckage was discovered at the Indian Ocean island of La Reunion. – Astro AWANI

The majority of passengers on board MH370 were from China.

"No matter whether or not we confirm that this debris is from MH370, it should not influence the different parties' commitments -– the search for MH370 should not be given up," the statement added.

Hong Xiufang, whose son, daughter-in-law and granddaughter were on the plane, added earlier: "The manpower and other resources they have thrown into this (search) is huge, but what they have found is so little and it may still not be the (plane's) debris.

"So many countries were searching for the plane, but none have found it, or any debris, so why have they suddenly found the debris now?" Hong added. "Us relatives all don't believe this matter."

Malaysian Selamat Omar, whose son Mohamad Khairul, 29, was on MH370, called on the his country's government to be more aggressive in its search for the plane.

"We need to find the main frame of the aircraft and the bodies. Until then I will continue to believe that my son is alive and not dead," Omar said.

Jacquita Gonzales, the Malaysian wife of Patrick Gomes, the flight's cabin crew supervisor, said the news had set her on an emotional rollercoaster.

"It has started all over again, staring at the handphone constantly for news," she said.

"I am just trying to keep my mind busy with other things and wait for the relevant people to at least let me know what's going on.

"We are just waiting again, like before."