Kanye West is pressuring Billie Eilish, and holding Coachella fans hostage in the process ... threatening to pull out of the festival if she doesn't say she's sorry for an apparent jab at Travis Scott.

Ye just posted a manifesto, of sorts, demanding -- in all caps -- the 20-year-old singer "APOLOGIZE TO TRAV AND TO THE FAMILIES OF THE PEOPLE WHO LOST THEIR LIVES."

You'll recall, last week BE stopped her concert in Atlanta to make sure a fan near the front row was okay, as they were having trouble breathing. Then came the shot at Travis -- "I wait for people to be okay before I keep going."

Well, now Ye's coming to Travis' defense, saying ... "TRAV DIDN'T HAVE ANY IDEA OF WHAT WAS HAPPENING WHEN HE WAS ON STAGE AND WAS VERY HURT BY WHAT HAPPENED."

As you know, Ye and Billie are both scheduled headliners at Coachella this year -- and in his post, Ye says he plans to bring Travis with him to the festival ... that is, IF he goes now.

As he threatened, "NOW I NEED BILLIE TO APOLOGIZE BEFORE I PERFORM."

It's unclear if Ye meant Travis would be onstage performing with him, or if he'd just be there for moral support. Either way, Mr. West is now bullying Billie and, in a way, Coachella.