JAKARTA (Reuters) - Families of some of the 189 people killed in a Lion Air plane crash held a protest rally in Indonesia on Thursday, while stalled efforts to bring the main wreckage to the surface and find the second black box are set to resume next week.

FILE PHOTO: A personnel from National Transportation Safety Board examines debris from Lion Air flight JT610 at Tanjung Priok port in Jakarta, Indonesia, November 1, 2018. REUTERS/Beawiharta/File Photo

The Boeing Co 737 MAX jet crashed into the Java Sea on Oct. 29 shortly after take-off from Jakarta, but the families expressed concern that the remains of 64 passengers have yet to be identified, with just 30 percent of the plane’s body found.

About 30 people attended a rally outside the presidential palace in Jakarta, holding placards calling for Lion Air to put safety over profit and for President Joko Widodo to ensure the remains are recovered.

“Maximum efforts have not been done,” said Johan Hari Saroinsong, whose son Hizkia died in the crash. “It is shallow water in the Java Sea only 35 meters deep.”

Lion Air is paying for a specialized ship to help lift the main wreckage of flight JT 610 and give investigators a better chance of finding the cockpit voice recorder (CVR) in a search that has lacked sophisticated equipment for the last month, Reuters reported.

Indonesia’s national transport panel said the vessel was due to arrive on Monday.

The enhanced search will cost $2.8 million for the first 10 days, a source close to the airline said on Thursday, on condition of anonymity, adding that Lion Air is paying because the government does not have the budget.

“Funds for the CVR search will be borne by Lion Air which has signed a contract for a ship from a Singaporean company,” a finance ministry spokesman told Reuters.

The family members are seeking daily updates from Lion Air on the search, according to a letter addressed to Widodo and distributed by the group at the rally.

The families asked the airline for financial assistance so they could stay in Jakarta during the search, and for immediate compensation in line with regulations. They also want the government to ensure Lion Air keeps its promises.

Lion Air’s decision to foot the bill for the search is a rare test of global norms regarding search independence, as such costs are typically paid by governments.

In this case, investigators said they had faced bureaucratic wrangling and funding problems before Lion Air stepped in.

Safety experts say it is unusual for one of the parties to help fund an investigation, required by U.N. rules to be independent, so as to ensure trust in any safety recommendations made.

There are also broader concerns about resources available for such investigations worldwide, coupled with the risk of agencies being ensnared in legal disputes.

The clock is ticking in the hunt for acoustic pings coming from the L3 Technologies Inc cockpit voice recorder fitted to the jet. It has a 90-day beacon, the manufacturer’s online brochure shows.

The flight data recorder was retrieved three days after the crash, providing insight into aircraft systems and crew inputs, although the cause has yet to be determined.