The Malaysia Airlines jet vanished in March 2014 with 239 people -- mostly from China -- on board, en route from Kuala Lumpur to Beijing.
No sign of the plane was found in a 120,000 square kilometre (46,000 square mile) sea search zone and the Australian-led hunt, the largest in aviation history, was suspended in January last year.
After pressure from family members, the former Malaysian government struck a deal with US exploration firm Ocean Infinity to restart the search on the condition it would only be paid if the jet or its black boxes were found.
The firm, which deployed hi-tech underwater drones in its hunt, stood to make up to $70 million if successful.
Malaysia's Transport Minister Anthony Loke, part of the new government that came to power following May 9 elections, said the hunt was officially meant to finish in April but had been extended, and would come an end next week.
"The search will continue until May 29," he told reporters.
Prime Minister Mahathir Mohamad had said earlier that the contract with Ocean Infinity was being reviewed.
"We can't tell (the government) what to do but for me and the families... finding the plane is important for many reasons," she told AFP.
The new hunt started late January in an area of about 25,000 square kilometres in the southern Indian Ocean, north of the former search area.
The ship conducting the hunt, Seabed Constructor, was a Norwegian research vessel carrying 65 crew, including two members of the Malaysian navy as the government's representatives.
It used eight autonomous drones, equipped with sonars and cameras, that scoured the waters for wreckage and can operate in depths up to 6,000 metres (20,000 feet).
However it did not find any sign of the jet.
Only three confirmed fragments of MH370 have been found, all of them on western Indian Ocean shores, including a two-metre wing part known as a flaperon.