Watch "Vanished: The Mystery of Malaysia Airlines Flight 370" Friday at 10 p.m. ET.
A U.S. official said it was likely the wreckage came from a Boeing 777 like MH370, while Malaysian Transport Minister Liow Tiong Lai said there was a "high possibility" the part came from that type of plane. Malaysia Airlines Flight 370 is the only 777 to be missing in the region where the piece was found.
Others are being more skeptical. Cmdr. Joao Abreu, the chief executive of the Mozambique Civil Aviation Authority, told CNN's David McKenzie that the piece of debris might belong to a "medium-sized plane" and not a 777. Abreu noted that there is no marine life of any kind or major wear and tear on the piece, as would be expected after nearly two years in the ocean. Still, he is not ruling anything out until the piece is analyzed further.
In early March 2014, Flight 370 took off from Kuala Lumpur, Malaysia, en route to Beijing with 227 passengers and 12 crew members on board. It vanished from radar in airspace over the Gulf of Thailand.
After so many false alarms and theories for the disappearance of the plane, family members of the victims are treating this new report with a great deal of suspicion, and even anger.
MORE: The last moments of MH370
"Just like previous cases of suspected debris, I always think that we need to wait for various authorities to verify, confirm (what the item actually is) and to show us concrete evidence," Steve Wang, whose mother was one of the 239 passengers aboard the flight, told CNN.
"(The debris is) all so scattered to such a wide span of areas, it is hard to see how one piece can really help," he said.
Zhang Meiling, who lost three family members, had stronger words: "We don't believe in the stories of debris anymore."
What did they find?
The piece of debris suspected to be from MH370.
The wreckage is a piece of horizontal stabilizer skin, the U.S. official said, the part of the aircraft's tail that stays horizontal as the plane flies.
It measures about 35 inches by 22 inches (89 centimeters by 56 centimeters) and is apparently from a Boeing 777, like the missing MH370 airliner.
The debris includes a fastener, which an executive at fastener company LISI Aerospace said is a pretty standard part.
"I would expect to see this on many varieties of Boeing aircraft, not particular to a 777," said Jared Young, vice president of research and development.
An aviation source said there was no record of any Boeing 777 missing other than Malaysia Airlines Flight 370.
Debris found in Thailand in mid-January turned out to be unrelated.
Who found it?
American Blaine Gibson had chartered a boat for a weekend trip off the coast of Mozambique and found the plane part washed ashore on a sandbar after the boat's captain spotted it.
READ: Tourist searching for MH370
He is also part of an independent group that interpreted data in a bid to find the missing plane.
"What went through my mind when I found it is that this is something that could be part of an airplane and could be part of that airplane," Gibson told CNN.
"Anything that can help lead to the truth of what happened and get the families the answers that they long for and deserve no matter what they are, whatever the truth is, anything that leads to that, is very good and needs to be done," he said.
It's not unusual for private people and companies to get involved in searches for missing planes, especially when the search has gone on for a long time.
After the underwater search for MH370 was postponed, Australia said it would negotiate with private contractors to conduct the next phase. Authorities chose the Dutch firm Fugro Survey to carry out the Indian Ocean search.
'Violent breakdown'?
The discovery was reported to officials Monday, and Gibson handed over his find to Mozambique authorities. The piece will be sent to Australia for examination.
While it took more than a month for French investigators to confirm that debris found on Reunion Island last July was from the missing plane, Geoffrey Thomas, managing director of Airline Ratings, said confirmation should take just a few days.
READ: 'Certainty' that Reunion Island debris is from MH370
Thomas added that the debris was found "in the right area" -- a location consistent with modeling done by the University of Western Australia that suggests the plane went down over the southern Indian Ocean.
If confirmed, it suggests a violent breakdown and discounts a theory that a rogue pilot gently took the plane into the water to mask his intentions of crashing it, Thomas said.
Two-year wait for answers
The discovery comes just days before the second anniversary of the disappearance of the flight, which took off on March 8, 2014.
The two-year mark carries extra significance because it's the last day for families to file for airline compensation.
Under international treaties, families have to make a claim against the airline within two years. But for them to do that, they would have to admit that their loved ones are dead, which many are unwilling to do.
"We have not picked up any compensation, we simply want our man back!" said Ye Lun, whose brother-in-law was a passenger.
MORE: MH370 family member: 'I can't speak'
Voice 370, a family support group, said an event would be held Sunday at The Square in Publika, Kuala Lumpur, Malaysia.
"The families and friends of passengers on board MH370 have endured a long wait of two years for reliable news on the whereabouts of MH370 and the fate of our loved ones on board," the group said, calling for funds and for the search to continue.
The international search effort is expected to conclude by midyear.
CNN's Yuli Yang, Rene Marsh and Don Melvin contributed to this report.
