Trump called Boeing chief executive Dennis Muilenburg on Sunday for details about the MAX production plans, the person said, confirming reports in U.S. media.
Chao said of Boeing: "They've got a tough challenge ahead of them and they owe it to the American people to ensure that their airplane is safe".
Boeing said earlier this month it will suspend production of the aircraft temporarily to focus on delivering the some 400 MAX planes it has since built. It did not say when production would resume.
Earlier on December 20, Spirit AeroSystems (NYSE: SPR) of Wichita, Kansas, announced it will stop building fuselages for the 737 MAX on January 1, as the effects of the aircraft's grounding following two deadly crashes extend down the supply chain and begin to impact the broader economy.
The entire fleet of 737 MAX aircraft was grounded after two fatal crashes within months of each other killed 346 passengers and crew.
The continuing delay in returning the 737 to service caused United Airlines on Friday to pull the plane from its flight schedule until June.
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Chao also said the White House Council of Economic Advisers had conducted a study of the economic impact of the grounding, which forced Boeing - a critical American manufacturing company - to halt deliveries in March, and assessed that it would cause around a 0.4% reduction in United States gross domestic product.
United expects to cancel about 75 flights per day this month and 56 flights per day in January.
The planemaker had so far shielded major MAX suppliers from a financial hit following the grounding, continuing to purchase parts from suppliers at a rate higher than its own, in order to keep the supply chain running and avoid major disruptions when the MAX returns to service. United is scheduled to receive 28 more 737 MAXes next year.
Spirit did not say how the production suspension would affect its workforce of more than 13,000 people.
Technical fixes to the Max should have taken just a couple of months, but political and regulatory pressure have contributed delays, he added.
This week, Kansas Gov. Laura Kelly said that the state may have to help pay workers at a company if the planes don't return to the sky soon. "Everything has to be investigated and gone over and over again and again". Shares of Boeing fell 1% while Spirit AeroSystems Holdings Inc. slid 0.5% Friday.