Relatives of the victims confronted Lion Air co-founder Rusdi Kirana at a meeting organized by officials on Monday.
Tjahjono said his agency was asking Boeing and the United States what action to take to prevent similar problems around the world.
The cockpit voice recorder could offer crucial clues, he said, noting that besides conversations inside the cockpit, it could also contain other valuable information, such as warning sounds.
Indonesia's National Transportation Safety Committee said it had agreed with Boeing on procedures that the airplane manufacturer should distribute globally on how flight crews can deal with "angle of attack" sensor problems. "Imagine if you were in our position", said Najib Fuquoni, a relative of a victim, demanding an independent investigation into the crash.
"Data from the black box showed that two flights before Denpasar-Jakarta also experienced the same problem", he said.
"This is not an unimportant thing. Hopefully with the remaining time we can search until the 10th day", a visibly emotional Syaugi said, as he choked and struggled to hold back his tears. Of course, this is something they already overwhelmingly do, as we can see from the generally incredible recent safety record in global aviation, but clearly something went very wrong here that shouldn't have.
The investigation is now focused on flight data from one of the black boxes, found last week. He did appear at the meeting, standing with his head bowed, according to the Associated Press.
The privately owned budget carrier was founded in 1999. "We had to wait inside the aircraft for about 20 minutes with the air conditioner not working".
Malfunctioning AOA sensors could cause the 737 MAX to try and automatically push down the nose of the airplane if they detect that an aerodynamic stall is possible, a person familiar with the matter told Bloomberg. Boeing has more than 4,500 unfilled orders for the 737 Max on its books.
Divers have been retrieving bodies for days, and the search efforts continue.
Lion Air Flight 610 crashed in the Java Sea shortly after taking off from Jakarta, Indonesia, on October 28.
Indonesian authorities have downloaded information from the flight data recorder that showed a cockpit indicator on the Lion Air jet was damaged for its last four flights.
Indonesian investigators said this week that the plane had an air-speed indicator problem on the doomed flight and on three previous journeys.
The KNKT added that the FDR's recordings were 69 hours from 19 flights and the last date of recording was from the date of the crash and corresponded with public data available on flight-tracking websites.
Search teams combing the wreckage of JT610 have filled 186 body bags with remains but only 44 victims have been identified so far.
They will focus on a 250m radius in the Java Sea where plane parts - including wheels and turbines - have been found.
On Monday, Indonesian authorities said the aircraft was flying at high speed when it crashed into the sea on October 29, causing an huge impact. Data transmitted from the plane and captured by flightradar24.com indicates that the plane continued flying at high speed away from the airport to which they meant to return, which Cox said seemed unusual.