“I ask you not to sacrifice the opportunity to secure our future together, because of the frustrations of the past,” said Mr Ortberg in his message to staff.
“Working together, I know that we can get back on track, but a strike would put our shared recovery in jeopardy”.
On top of the proposed 25% pay rise, the preliminary deal would offer workers improved healthcare and retirement benefits, as well as 12 weeks of paid parental leave.
It would also include a commitment from Boeing to build its next commercial plane in the Seattle area if the project is started during the lifetime of the contract.
The union initially targeted a number of improvements to workers’ packages, including a 40% pay rise.
However, it appears the reaction from the 30,000 Boeing workers represented by the union was not entirely positive.
Union leader and top negotiator, John Holden, said it was not clear whether the deal had enough support among union members to be approved.
“They are angry,” he told the Reuters news agency.
The current contract between Boeing and the unions was reached in 2008 after an eight-week strike.
In 2014, the two sides agreed to extend the deal, which is due to expire at midnight on Thursday.
A rejection of the preliminary agreement between Boeing and its largest union would be a further significant setback for the firm.
A strike could potentially shut down aircraft production at a time when the company is facing deepening financial losses and struggling to repair its reputation following recent incidents and two fatal accidents five years ago.
It would also be a major blow to Mr Ortberg, an aerospace industry veteran and engineer, who took over as Boeing’s chief executive last month with a mission to turn the business around.