The message suggests everything was normal on board minutes before the plane went missing over the South China Sea.
Flight MH370 replied: “All right, roger that” to a radio message from Malaysian air control, authorities said.
The search has been widened to waters off both sides of the peninsula.
Malaysia’s air force chief has denied reports the plane was tracked to the Malacca Strait in the west.
The China-bound plane went missing on Saturday with 239 people on board.
The plane vanished about an hour after it took off from Kuala Lumpur International Airport, as it flew over the South China Sea, south of Vietnam’s Ca Mau peninsula. No distress signal or message was sent.
Malaysian authorities revealed the plane’s last communication at a news conference held in Beijing for relatives of the 154 Chinese who are among the missing passengers.
As the plane reached the boundary between Malaysian and Vietnamese airspace, the Malaysian air control announced it was handing over to Ho Chi Minh City Control.
Minutes later, all contact with Flight MH370 was lost.
China’s foreign ministry said there was “too much confusion” regarding the information released about the plane’s flight path.
“It is very hard for us to decide whether a given piece of information is accurate,” spokesman Qin Gang told reporters in Beijing.
Earlier on Wednesday, Malaysia’s air force chief Rodzali Daud denied remarks attributed to him in local media that flight was tracked by military radar to the Malacca Strait, far west of its planned route.
Gen. Rodzali Daud said he “did not make any such statements”, but the air force had “not ruled out the possibility of an air turn-back”.
Early search efforts focused on waters between Malaysia and Vietnam.
The search was later extended to the Malacca Strait and the Andaman Sea, off Malaysia’s west coast, amid reports that the plane could have turned back.
Operations are now covering some 27,000 square nautical miles.
Malaysian authorities on Wednesday requested assistance from India in searching the Andaman Sea, north of the Malacca Strait.
Vietnam has confirmed an investigation into a possible sighting of the plane has so far yielded no results.
Vietnam’s air traffic management earlier said it had received an email from a New Zealander working in one of the oil rigs off Vung Tau.
“He said he spotted a burning [object] at that location, some 300 km [200 miles] southeast of Vung Tau,” deputy general director Doan Huu Gia said.
Officials still do not know what went wrong with the aircraft, and several leads pursued so far have proven not to be linked to the plane.
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