Three pieces were found by American lawyer Blaine Gibson on the island of Nosy Boraha, off the east coast of Madagascar.
Another was found Thursday by Samuel Armstrong amid seaweed and wood on Kangaroo Island, off the coast of South Australia, CNN affiliate Seven News reported
The Joint Agency Coordination Center,
the agency in charge of coordinating the search for MH370, said in a statement that it "is aware of these reports" that possible debris had been found.
Gibson had been filming with public television channel France 2 when he and the crew came across what appear to be pieces of the Boeing 777 which disappeared in March 2014 with 239 people on board.
Earlier this year, Gibson found a piece of a plane wreckage
off the Mozambique Coast, while on a self-funded hunt for the missing plane. Australian investigators later said it "almost certainly"
came from MH370.
The largest piece of new debris measures approximately 50 centimeters by 77 centimeters. Gibson said it "very much resembles the 'No Step' panel I found in Mozambique -- same color, same texture on both sides."
The second piece had the letters "FB" stenciled onto it.
Gibson believes the other, and most significant piece of debris, is a frame of a screen monitor. He said there are three small barnacles on the back of it, which could provide clues to investigators as to the time it's been in the sea and the route it traveled.
"I have to tell you this that the monitor screen touched me very deeply and brought tears to my eyes because this is what you see as you sit on the plane on the seat in front of you. This is very graphic," he said.
Search to end soon
Flight MH370 disappeared from radar while en route from Malaysia to Beijing. A search in the southern Indian Ocean, thousands of kilometers off the west coast of Australia, has failed to find any trace of the plane.
Search operations have been suspended for the past four weeks because of poor weather conditions, the Australian Transport Safety Bureau (ATSB) said
"It may take until around August to complete the 120,000 square kilometers, but this will be influenced by weather conditions over the coming months, which may worsen," it said.
No more official efforts to find MH370 are planned if the plane does not turn up in that search zone.
Gibson is hopeful that, failing the discovery of the plane in the official search zone, his latest finds will prompt them to extend the search.
The zone has been set off the interpretation of satellite data from Inmarset, he explained. But he suspects it should be farther north or northwest.
"We must solve this mystery and give the families the answers they deserve," he said.