But the US aerospace giant gave no further details about when the grounded aircraft is likely to return to the skies, during the release of its Q1 financial results.

The 737 MAX has been grounded worldwide since last month following a fatal crash of an Ethiopian Airlines aircraft on March 10 – the second deadly crash of a 737 MAX within six months.

Boeing said it had completed more than 135 test and production flights using the software update, which is designed to correct a technical fault believed to be the cause of both crashes.

Dennis Muilenburg, Boeing’s chief executive, said: “Across the company, we are focused on safety, returning the 737 MAX to service, and earning and re-earning the trust and confidence of customers, regulators and the flying public.”

Boeing said it was continuing to work closely with global regulators and airlines “to comprehensively test the software and finalise a robust package of training and educational resources” to allow the 737 MAX to return to service.

The company revealed the crisis had reduced revenue at its Commercial Airplanes division by more than $1 billion during the first quarter of 2019. Revenue dropped from $12.9 billion to $11.8 billion year-on-year as the Boeing temporarily reduced production of the 737 MAX in the quarter.

Boeing also admitted it could not currently give any forecasts about how much the grounding would cost the company due to “the uncertainty of the timing and conditions surrounding return to service of the 737 MAX fleet”.

The grounding of the 737 MAX continues to cause problems for many airlines which rely on the aircraft – Norwegian said the grounding could prevent its planned return to profit this year and the low-cost carrier has also agreed a deal with Boeing to postpone a delivery of 14 737 MAXs.

The worldwide fleet of 737 MAX had reached 387 aircraft at the time of the grounding in March.

Boeing only delivered 89 of the aircraft during the first three months of the year, down from 132 deliveries in the same quarter of 2018.