Last week, Malaysia, China and Australia said in a joint statement that the hunt for MH370 would be suspended if the aircraft was not found in an area now being searched.
The Boeing 777, with 239 aboard, disappeared in March 2014 while on a flight from the Malaysian capital, Kuala Lumpur.
Almost A$180 million ($135 million) has been spent since then on an underwater search spanning 120,000 square kilometres (46,332 square miles) in the southern Indian Ocean.
About 30 family members, some in tears, gathered at Chinas foreign ministry to hand over the petition, and a group were allowed in despite a brief stand-off with plainclothes security.
"We oppose their decision. We dont recognise it at all. That decision has no reason behind it," said Boa Lanfang, 65, whose son, daughter-in-law and grandson were on the flight.
Some family members held up placards reading "The three governments have an obligation to the world to fulfil their promise".
The families of those on board, most of whom were from China, have pressed hard for answers ever since the plane went missing.
Chinas Foreign Ministry did not immediately respond to a request for comment, Reuters reported.
Investigators believe the plane was deliberately flown thousands of kilometres (miles) off course before crashing into the southern Indian Ocean off Australia.
Malaysian investigators said in 2015 there was nothing suspicious in the financial, medical or personal histories of pilots or crew.
Several pieces of aircraft wreckage have washed up on beaches in Africa and been positively identified as coming from MH370 but they shed little light on the mystery.
The search has lasted more than two years but has found no sign of the main wreckage.
Editor: Priyambodo RH
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