So far six Malaysian families and one Chinese family have received the money, and insurers are assessing the claims of 40 more Chinese families.
Relatives of all 239 missing passengers can claim up to $175,000 each.
Flight MH370 went missing on 8 March as it flew from Kuala Lumpur to Beijing. No trace of the plane has been found.
Malaysian deputy foreign minister Hamzah Zainudin stressed that the government has not yet declared the plane lost.
“When we talk about the full payment, we have to wait until we announce the issue on the tragedy MH370 is over,” he said.
Malaysia Airlines’ insurer, a consortium led by Germany’s Allianz, is making the payments.
Many of the relatives also refuse to accept that their relatives may be dead.
A group of families has joined together to raise $5m (£2.9m) to investigate the plane’s disappearance and encourage anyone who might have information to come forward.
A massive search operation conducted in seas hundreds of miles from any land has failed to find any debris from the plane.
Experts are continuing to survey the sea floor and are bringing in specialist equipment.
They believe the jet ended its journey in the Indian Ocean, hundreds of miles north-west of the Australian city of Perth.