The aircraft disappeared between Kuala Lumpur and Beijing on 8 March 2014 with 239 people on board.
Australian-led search teams are combing a 120,000 sq km (46,330 sq mile) area of the southern Indian Ocean.
Only one confirmed piece of debris, a part of wing called a flaperon, has been found, on Reunion Island.
The search, involving Australian, Chinese and Malaysian experts, is estimated to have cost more than $130m (£92m).
The countries have said it will end once the current search area has been completely covered, likely to be around June.
In a statement on Tuesday, Malaysian Prime Minister Najib Razak said he remained “hopeful that MH370 will be found”, but once the search zone is exhausted the three governments would meet to determine the way forward.
“We remain committed to doing everything within our means to solving what is an agonising mystery for the loved ones of those who were lost,” he said.
But Martin Dolan, head of the Australian Transport Safety Bureau (ATSB) which is co-ordinating the search, told the BBC the governments’ positions were unchanged and the search would end then, “unless new and significant information comes to light”.
Many relatives want the operation to continue until the plane is found.
Australian Transport Minister Darren Chester also expressed hope on the anniversary, saying finding the plane would “give answers to the world, in particular the families of missing loved ones, about what happened”.
On Monday, relatives of 12 Chinese passengers filed lawsuits in Beijing.
Lawyer Zhang Qihuai said they were seeking a range of damages, but their goal was to determine the cause of the accident and those who were responsible.