Describing the disaster as a "tragic day" in a "tragic year" for Malaysia, Najib Razak said the investigation "must not be hindered in any way".
The plane, now known to have been carrying 298 people, crashed in rebel-held territory near the Russian border.
Both sides in Ukraine's civil conflict have accused the other of shooting it down with a missile.
The Boeing 777, with the call sign MH17, was flying from Amsterdam to Kuala Lumpur.
It is the second disaster suffered by Malaysia Airlines this year. Flight MH370 disappeared en route from Malaysia to China in March and has still not been found.
In a statement, Malaysia Airlines said MH17 was carrying at least 154 Dutch nationals, 27 Australians, 43 Malaysians (including 15 crew), 12 Indonesians and nine Britons.
Other passengers came from Germany, Belgium, the Philippines and Canada, with the nationalities of 41 people not yet confirmed.
Several of those on board were heading for a major international conference on HIV/Aids in Melbourne, Australian officials said.
Other airlines have announced they are now setting flight paths to avoid eastern Ukraine.
'Swift justice'
In his statement, the Malaysian leader said the plane's route had been declared safe by the International Civil Aviation Organization.
He said the plane had not made a distress call.
"Malaysia is unable to verify the cause of this tragedy. But we must - and we will - find out precisely what happened to this flight," Najib said.
"If it transpires that the plane was indeed shot down, we insist that the perpetrators must swiftly be brought to justice."
Malaysia is sending a team to Ukraine to help with the investigation.
US and Ukrainian officials said they believed the plane had been brought down by a missile.
Ukrainian President Petro Poroshenko said it was an "act of terrorism".
But Russian President Vladimir Putin blamed the Ukraine government for restarting military operations in the area, where it is trying to regain control from pro-Russian rebels.
"The country in whose airspace this happened bears responsibility for it," he said.
Separatist leader Alexander Borodai, meanwhile, accused the Ukrainian government of bringing down the airliner.
In a telephone conversation, US President Barack Obama and the Dutch leader, Mark Rutte, "agreed on the need to assure immediate access to the site... to international investigators... to carry out a thorough investigation".
'Mistake or terrorism'
The plane fell between Krasni Luch in Luhansk region and Shakhtarsk in the neighboring region of Donetsk.
The head of the Russian Air Traffic Controllers' Union, Sergei Kovalyov, said Russian that the airspace over eastern Ukraine had remained open during the conflict because the planes previously shot down had tended to be helicopters or low-flying fast jets.
"In order to bring down an airplane from an altitude of 10,000m, you need to have very serious weapons…. missiles," he said.
"It's either a mistake or a terrorist act."
Ukraine has accused Russia's military of supplying advanced missiles to the rebels.
Earlier on Thursday, Ukrainian officials blamed the Russian air force for shooting down one of its ground attack jets on Wednesday, and a transport plane on Monday.
In 2001, Ukraine admitted its military was probably responsible for shooting down a Russian airliner that crashed into the Black Sea, killing all 78 people on board.
BA/BA