(Reuters) -Boeing's largest union urged new CEO Kelly Ortberg on Tuesday to get more involved in contract negotiations to end a strike by around 33,000 U.S. West Coast workers, after the U.S. planemaker cut off their healthcare benefits.

In August, the former Rockwell Collins boss took over the reins of Boeing, which has been rocked by multiple crises this year, including the strike that has hit production of Boeing's strongest-selling 737 MAX jets.

"It's time for the new CEO to truly engage at the proposal-based level and to take the reins from his subordinates who are fumbling critical decisions like this one," said Brian Bryant, president of the International Association of Machinists (IAM) and Aerospace Workers, which represents the striking workers.

"There is no reason the health benefits question could not have been punted on to allow more time for negotiations at the table," Bryant added in a statement.

The Sept. 30 limit for striking workers to access their Boeing health insurance plans was long known, with the union urging workers on Monday to find alternatives.

Talks between Boeing and the IAM's District 751, which is negotiating the deal, broke off last week and it is not clear when discussions will resume.

"We remain committed to resetting our relationship with our represented employees and negotiating in good faith, and want to reach an agreement as soon as possible," Boeing said in a statement.

Boeing workers in the Seattle area and Portland, Oregon, walked off the job on Sept. 13 in the union's first strike since 2008, halting production of three commercial airplane models and adding financial strain to the planemaker.

The union is seeking a 40% pay rise and the restoration of a defined-benefit pension that was taken away in the contract a decade ago.

Boeing made an improved offer last week to the striking workers that it described as its "best and final", which would give workers a 30% raise over four years and restore a performance bonus, but the union said a survey of its members found that was not enough.

(Reporting by Allison Lampert in Montreal and David Shepardson in Washington; Editing by Muralikumar Anantharaman)