April 4 (Reuters) - The U.S. Justice Department next week will meet with lawyers for families of victims of two fatal Boeing 737 MAX crashes that killed 346 people in 2018 and 2019, as the government decides whether to move ahead with a criminal case, according to correspondence Reuters reviewed.

The meeting, set for Tuesday afternoon, comes ahead of an April 24 gathering scheduled for the victims' families themselves to confer with Justice Department officials.

"As we have ... done previously, we think it would be productive to hold a lawyers-only meeting approximately two weeks before the conferral," said Glenn Leon, the Justice Department's fraud section chief, in an email to lawyers for victims' families Reuters reviewed.

Boeing declined to comment. A Justice Department spokesperson had no immediate comment.

Boeing won immunity from criminal prosecution over the fatal 737 MAX crashes as part of an agreement reached with the Justice Department in January 2021 that involved the company paying $2.5 billion to resolve a fraud conspiracy charge related to the plane's flawed design. Boeing had to abide by the terms of the agreement for a three-year period that ended on Jan. 7.

Two days before the settlement's term expired, on Jan. 5, a piece of fuselage tore off the left side of a Boeing 737 MAX 9 as an Alaska Airlines flight climbed above 16,000 feet in the air. No one was killed.

The Justice Department has until July 7 to decide whether Boeing abided by or violated any terms of the 2021 agreement stemming from the 737 MAX fatal crashes.

The Justice Department is investigating whether Boeing violated the 2021 deal with prosecutors, which imposed a host of conditions on the company that included strengthening its compliance program, a person with knowledge of the matter told Reuters. A violation could allow the Justice Department to prosecute a criminal case against Boeing.

The Tuesday meeting and subsequent April 24 gathering of Justice Department officials, victims' families and their lawyers is related to the 737 MAX fatal crashes, as opposed to the mid-air blowout involving the Boeing plane during the Alaska Airlines flight in January.

Nevertheless, the meetings come against the backdrop of increased government pressure and scrutiny of Boeing following the more-recent mid-air emergency. In the case of the previous fatal crashes involving Boeing planes, victims' families have criticized the settlement that put the company on a path to avoiding criminal prosecution.

The FBI on March 19 told passengers on the Alaska Airlines Boeing 737 MAX 9 flight that they may be victims of a crime, according to letters seen by Reuters. The letters said the FBI has identified the passengers "as a possible victim of a crime. This case is currently under investigation by the FBI ... A criminal investigation can be a lengthy undertaking, and, for several reasons, we cannot tell you about its progress at this time."

(Reporting by Mike Spector and Chris Prentice in New York, and David Shepardson in Washington. Additional reporting by Allison Lampert in Montreal, Editing by Nick Zieminski)