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The Federal Aviation Administration on Monday said U.S. airlines can still fly the Boeing jet model that has been involved in two crashes in less than six months.

Its announcement came as other countries around the world — including Australia, China, Singapore, Indonesia, Argentina and Mexico's Aeromexico — grounded the Boeing 737 Max 8 and 737 Max 9 jets in their airlines' fleets in the wake of an Ethiopian Airlines crash that killed all 157 people aboard Sunday.

The 737 Max 8 that went down in Ethiopia shortly after takeoff is that same model that crashed in Indonesia in late October, killing 189.

The FAA said the 737 Max 8 and its newer version, the Max 9, are airworthy. It also said it will closely examine all crash data in Ethiopia and take action if it is warranted.

"All data will be closely examined during this investigation, and the FAA will take appropriate action if necessary," the agency said in a statement.

The agency noted that reports are drawing similarities between this accident and the Indonesia crash, but said "this investigation has just begun, and to date we have not been provided data to draw any conclusions or take any actions."

Besides the FAA, commercial airlines in the U.S. and Boeing were all coming under pressure Monday to keep 737 Max jets out of the air or at least to address safety concerns while the crash investigation is ongoing.

Boeing announced Monday night that enhancements to flight-control software for its 737 Max fleet would be implemented in the "coming weeks," Reuters reported.

The company said the updates, which it began developing after the Indonesia crash in October, include tweaks to pilot displays and changes to crew training and operation manuals, the company said in a statement.

Earlier in Monday, Sen. Dianne Feinstein, D-Calif., was among those calling for the FAA to ground the 737 Max-8 jets used by U.S. airlines.

“This aircraft model represents only a small fraction of the domestic fleet, and several other countries have already taken this important step, including China and Indonesia," she said.

Chicago-based Boeing says on its website that the 737 Max 8 and Max 9 models are “the fastest-selling airplane in Boeing history.” It says it has received “nearly 4,700 orders from more than 100 customers worldwide” for the jets.

The company has built 329 of the 737 Max 8 series and 21 of the Max 9 models, according to the FAA.

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Jim Hall, a former head of the National Transportation Safety Board, said on MSNBC that Boeing should ground all of these aircraft until they can be checked for safety.

Hall noted that Sunday’s catastrophe in the Ethiopian capital of Addis Ababa happened less than six months after the Lion Air crash in Jakarta, Indonesia, in late October.

“My personal feeling on this is that Boeing aircraft company ought to voluntarily itself ground these aircraft because of the similarities between these two accidents,” Hall said. “It’s a brand new aircraft, and we had such a remarkable safety record in aviation, that I think this blip needs to be addressed by the manufacturer, and they need to do a detailed — a detailed look, and with these black boxes available, that’ll be done in a short term.”

The union representing flight attendants meanwhile said Boeing, U.S. airlines, the NTSB and the FAA need to address safety concerns.

"Crew and passengers are expressing concern about the 737 MAX 8 following a second crash, with similar characteristics to the Lion Air Flight 610 crash," Association of Flight Attendants-CWA International President Sara Nelson said in a statement. "It is vitally important that U.S. airlines work with Boeing, the FAA, and the NTSB to address concerns and take steps to ensure confidence for the traveling public and working crews."

U.S. airlines that fly 737 Max 8 planes have not indicated any immediate plans to stop flying the jets.

In response to Twitter messages from apparently worried passengers, Southwest Airlines confirmed it has 34 of the 737 Max 8 version of the planes and is “confident in the safety of our fleet.”

"We remain confident in the safety and airworthiness of our entire fleet of more than 750 Boeing 737 aircraft, and we don’t have any changes planned to 737 MAX operations." the airline said in a statement.

American Airlines said it has 24 of the 737 Max 8 aircraft and that it will “closely monitor the investigation in Ethiopia.” In a subsequent statement, the airline said it continues to have "confidence in the safe operation of all of our aircraft, including the 737 MAX 8."

United Airlines said it doesn’t have any 737 Max 8 jets but has 14 of the 737 Max 9 versions in its fleet.

“We have made clear that the Max aircraft is safe and that our pilots are property trained to fly the aircraft safely,” a United Airlines spokesman said.

The Aviation Capital Group, which leases aircraft to airlines around the world, is also a Boeing customer, according to the company website. It was not immediately clear whether it owns the 737 Max 8, the Max 9 or both. NBC News reached out to Aviation Capital for comment but did not immediately hear back.

Canadian airlines such as WestJet, Sunwing Airlines and Air Canada also have 737 Max 8 jets or the Max 9 version in their fleets, according to the Boeing website.

The Air Canada pilots' association called on the government "to take proactive action to ensure the safety of the Canadian traveling public."

"No one is more invested in the well-being of passengers and crew than those who operate the aircraft upon which they fly," the pilots' association said in a statement.

On Monday, Argentina's airline pilots association halted its members from flying the jets, Reuters reported, while Mexican airline Aeromexico grounded its six 737 Max 8s. The company said in a statement that those flights would be covered by other planes in its fleet.

Similarly, China and Indonesia joined Ethiopia in halting the use of 737 Max 8 and Max 9 jets while the investigation of Sunday's crash is underway.

Chinese aviation authorities suspended the operation of all 737 Max 8 planes run by domestic airlines such as Xiamen and Shandong.

Singapore and Australia on Tuesday blocked all Boeing 737 MAX aircraft from using their airports.

In addition, Cayman Airways, which operates in the Caribbean and has regular flights to and from the U.S., said in a statement it, too, was suspending all 737 Max 8 flights “until more information is received.”

Boeing CEO Dennis Muilenburg sent a letter to employees on Monday that said the company was cooperating with the NTSB and Ethiopian authorities.

Muilenburg said the company has the “deepest sympathies” for the families of those who died on the Ethiopian Airlines flight and encouraged employees to “stay focused on the important work we do.”

“As we partner with regulators and the Ethiopian Airlines investigation unfolds, it’s necessary that we stay centered on the facts and avoid speculation,” the letter said. “Speculating about the cause of the accident or discussing it without all the necessary facts is not appropriate and could compromise the integrity of the investigation.”