Two fishermen claim they saw a plane flying low over the South China Sea that might be missing Malaysia Airlines Flight 370.

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(CNN) -- How could a commercial airliner disappear without a sign, you ask?

In fact, several people on the ground or at sea claimed they saw Malaysia Airlines Flight 370 before it went missing after its post-midnight takeoff from Kuala Lumpur on March 8.

The purported eyewitnesses include fishermen, an oil rig worker and islanders in an atoll. Some even alleged they saw it crash.

While none of their claims have been substantiated, their assertions add to the ongoing mystery of the missing Boeing 777 and the 239 people aboard.

Sighting claim: Kota Bharu, Malaysia

In the middle of the night, two fishermen near the Malaysia-Thailand border saw a plane flying low over the South China Sea -- at the same time that air traffic controllers lost contact with Flight 370 over the same body of water, at 1:30 a.m. or almost 50 minutes after takeoff.

Fisherman Azid Ibrahim and a friend had taken people fishing that night off the coast of Kota Bharu.

"I was fishing when I saw the plane -- it looked strange. Flying low. I told my friend that's not normal. Normally, it flies at 35,000 feet. But that night it touched the clouds. I thought the pilot must be crazy," Ibrahim said.

"It was really low. I saw the lights they looked like the size of a coconut," he said.

Their fishing grounds lay under a flight path, but the predawn plane was unusual to see because of its low altitude, they said.

The fishermen filed a police report about their sighting, but Malaysian officials haven't commented.

Sighting claim: Oil rig off Vietnam

A New Zealand man working on an oil rig off Vietnam claimed he saw a burning object in the sky Saturday morning, hours after the plane had taken off.

Mike McKay of New Zealand was stationed on the Sona-Mercur oil rig on seas about 186 miles southeast of Vung Tau, a coastal Vietnamese town outside Ho Chi Minh City, according to CNN affiliate Radio New Zealand.

McKay wrote of his sighting in an e-mail, the news outlet said.

"Gentlemen. I believe I saw the Malaysian Airlines flight come down. The timing is right. I tried to contact Malaysian and Vietnamese officials several days ago. But I do not know if the message has been received," he wrote last week. "I observed the plane burning at high altitude at a compass bearing of 265 to 275 degrees from our surface location.

"While I observed (the plane) it appeared to be in one piece. From when I first saw the burning (plane?) until the flames went out (at high altitude) was 10-15 seconds. There was no lateral movement so it was either coming toward our position stationary (falling) or going away from our location. The general position of the observation was perpendicular/south-west of the normal flight path and at a lower altitude than the normal flight paths," he wrote.

In fact, Vietnamese authorities dispatched aircraft last week to search for the plane, in response to McKay's report, the affiliate reported.

When the Vietnamese navy sent a plane to conduct a search, it found nothing, ABC News reported. Vietnamese naval officer Le Minh Thanh told that network that the plane investigated the area cited by McKay, but the search came up empty.

Sighting claim: Maldives atoll

On a remote island in the Maldives, residents claimed they saw a "low flying jumbo jet" the same morning that the Malaysia plane disappeared, according to the website of the Maldivian news outlet Haveeru.

Residents on the isle of Kuda Huvadhoo in the Dhaalu Atoll gave a description that matched the commercial airliners: white with red stripes, according to the news outlet.

"I've never seen a jet flying so low over our island before. We've seen seaplanes, but I'm sure that this was not one of those. I could even make out the doors on the plane clearly," an unidentified eyewitness said, according to Haveeru. "It's not just me either, several other residents have reported seeing the exact same thing. Some people got out of their houses to see what was causing the tremendous noise too."

These claims, published in a story Tuesday, were dismissed by Malaysian officials.

The Maldives coast guard told CNN it had no reports of such sightings and had not even been requested to conduct a search.

The acting Malaysian transport minister also declared the reports false.

"I can confirm that the Malaysian Chief of the Defense Force has contacted his counterpart in the Maldives, who has confirmed that these reports are not true," Minister Hishammuddin Hussein said at a press conference.

The Maldives Ministry of Defense and National Security also confirmed that their radar systems and surveillance mechanisms show no indication of the missing plane.

Sighting claim: Off Indonesia coast

Indonesian fishermen claim they saw an airplane crash around the Strait of Malacca on the morning of March 9 -- more than a full day after the Malaysian plane took off -- the Indonesian state news agency Antara reported late Monday.

The strait lies between Indonesia and Malaysia. The Indonesia fishermen, based in the North Sumatra provincial subdistrict of Pangkalan Susu, went to sea for a week of fishing on March 9, a Sunday.

At 11 a.m., they saw a plane crash, Antara reported.

"We saw an airplane crash around the Malacca Straits," a fisherman identified as Hendra said, according to Antara.

The fishermen saw a white plane crossing and circling, Antara reported. Smoke came from the plane's right rear portion when it circled for a second round and tilted to the left, the agency said.

Flying lower, the plane then fell from sight.

"We suspect the plane crashed into the sea," Hendra said, according to Antara. "We could not go to the location where the aircraft was lost due to large waves, and the boat did not have enough fuel."

The aircraft is believed to have crashed in waters off the Aceh provincial district of East Aceh.

But there are two problems with these fishermen's account.

They spotted the plane more than 24 hours after it took off from Kuala Lumpur, Malaysia.

And Indonesian military officials said their radar didn't spot Flight 370.

The Jakarta Post reported that Indonesian air force spokesman Air Commodore Hadi Tjahjanto said the Air Force's radar in Lhokseumawe, Aceh, didn't detect the missing flight in the area that the Malaysian military suggested was the plane's last detected position, around Penang waters.

"Our radar information has been shared with our Malaysian counterparts," the air force spokesman added, according to the Jakarta Post.

CNN's Saima Mohsin and Mitra Mobasherat in Malaysia and Sarita Harilela in Hong Kong contributed to this report. Michael Martinez reported and wrote from Los Angeles.

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