The air force planes were part of a multinational search operation launched after Flight MH370 fell off radar screens less than an hour after it took off from Kuala Lumpur for Beijing.
The oil slicks were spotted late on Saturday off the southern tip of Vietnam and were each between 10km (six miles) and 15km (nine miles) long, the Vietnamese government said in a statement.
There was no confirmation that the slicks were related to the missing plane, but the statement said they were consistent with the kinds that would be produced by the two fuel tanks of a crashed jetliner.
Two-thirds of the missing plane's passengers were from China, while others were from elsewhere in Asia, North America and Europe.
Malaysia Airlines chief executive Ahmad Jauhari Yahya said there was no indication that the pilots had sent a distress signal, suggesting that whatever happened to the plane occurred quickly.
Asked whether terrorism was suspected, Malaysian Prime Minister Najib Razak said: "We are looking at all possibilities, but it is too early to make any conclusive remarks."
Foreign ministry officials in Italy and Austria said the names of two nationals from those countries listed on the flight's manifest matched passports reported stolen in Thailand.
Italy's Foreign Ministry said the Italian man who was listed as being a passenger, Luigi Maraldi, was traveling in Thailand and was not aboard the plane. It said he reported his passport stolen last August.
Austria's Foreign Ministry confirmed that a name listed on the manifest matched an Austrian passport reported stolen two years ago in Thailand. It said the Austrian was not on the plane, but would not confirm the person's identity.
At Beijing's airport, authorities posted a notice asking relatives and friends of passengers to gather at a nearby hotel to wait for further information, and provided a shuttle bus service.
Relatives and friends of passengers were escorted into a private area at the hotel, but reporters were kept away. A man in a gray hooded sweatshirt later stormed out complaining about a lack of information. The man, who said he was a Beijing resident but declined to give his name, said he was anxious because his mother was on board the flight with a group of 10 tourists.
"We have been waiting for hours and there is still no verification," he said.
The plane was last detected on radar at 1.30am (5.30pm GMT on Friday) around where the South China Sea meets the Gulf of Thailand, authorities in Malaysia and Vietnam said.
Lai Xuan Thanh, director of Vietnam's civil aviation authority, said air traffic officials in the country never made contact with the plane.
The plane "lost all contact and radar signal one minute before it entered Vietnam's air traffic control," Lt Gen Vo Van Tuan, deputy chief of staff of the Vietnamese army, said in a statement.
Malaysian Prime Minister Najib Razak said that Malaysia had dispatched 15 planes and nine ships to the area, and that the US Navy was sending some planes as well. Singapore, China and Vietnam also were sending aircraft.
"In times of emergencies like this, we have to show unity of efforts that transcends boundaries and issues," said Lt Gen Roy Deveraturda, commander of the Philippine military's Western Command.
After the oil slick was spotted, the air search was suspended for the night, while the sea search was ongoing, Malaysia Airlines said.
The plane was carrying 227 passengers, including two infants, and 12 crew members, the airline said. It said there were 152 passengers from China, 38 from Malaysia, seven from Indonesia, six from Australia, five from India, three from the U.S., and others from Indonesia, France, New Zealand, Canada, Ukraine, Russia, Taiwan and the Netherlands.
In Kuala Lumpur, family members gathered at the airport.
"Our team is currently calling the next of kin of passengers and crew. Focus of the airline is to work with the emergency responders and authorities and mobilize its full support," said Mr Yahya.
"Our thoughts and prayers are with all affected passengers and crew and their family members."
Fuad Sharuji, Malaysia Airlines' vice president of operations control, told CNN that the plane was flying at an altitude of 35,000ft (10,670m) when it disappeared and that the pilots had reported no problem with the aircraft.
Malaysia Airlines has a good safety record, as does the 777, which had not had a fatal crash in its 19-year history until an Asiana Airlines plane crashed in San Francisco in July 2013, killing three passengers, all teenagers from China.