8:05 AM PT -- We just got Kanye out in NYC, and he's a LOT less chatty than he was Thursday night on Twitter. We asked him about the threats Drake made and he flashed us a big smile before sprinting to his car.

Kanye West and Kim Kardashian claim Drake has threatened to hurt their family -- and they're warning the rapper that if anything happens ... there will be hell to pay.

Long story short ... Kanye claims Drake called him on the phone Thursday and threatened physical harm.

"You threatened the safety of me and my family," Kanye posted on Twitter ... adding, "Never threaten north saint and Chicago’s dad bro."

Kim Kardashian entered the fray at 2:30 AM on Friday morning -- saying, "Drake Never threaten my husband or our family. He paved the way for there to be a Drake."

She added, "My husband is the most brilliant person, the most genius person that I know. He has broken so many boundaries, everything from music, stage design, fashion and culture and will continue to change the world."

So, how did this whole thing start?

Kanye posted a screenshot of his phone on Thursday that allegedly showed that someone from Drakes's team had reached out to clear one of Ye's songs for a project.

Kanye was upset because Drake has taken shots at him in various tracks recently -- yet still reached out to use his music -- and Kanye felt Drake was being a fraud.

Then, the Twitter storm began ... with Kanye going off on his issues with Drake.

"Been trying to meet with you for 6 months bro," Kanye said ... " You sneak dissing on [Travis Scott] records and texting [Kris Jenner] talking bout how’s the family."

Kanye says Drake eventually called him to talk Thursday night -- but it didn't go well.

"Drake called trying to threatened me."

Kanye then issued this warning -- "So drake if anything happens to me or anyone from my family you are the first suspect. So cut the tough talk."

Kanye said Drake is running around like he's 2Pac with no regard for human life or Kanye's family and acting like he's a hardcore gangster.

"You trying to be a bully. I never been bullied in my life and I never will be. That’s why I made it this far in a pink polo."

Despite the anger, Kanye tried to issue an olive branch at one point -- "I’m Ye bro Remember that I love you I would never intentionally hurt you That’s what I’ve been saying to you."

"You would be so sad if anything ever happened to me."

"I’m up for talking. We need to show all of these fans that black men can@talk without someone ending up dead or in jail."

"You are disrespectful to all people with mental health conditions so this is an opportunity for growth."

Drake hasn't said much publicly -- only posting some emojis on Instagram showing some crying/laughing faces.

Kanye has seemingly calmed down and is now at a meeting at J.P. Morgan Chase and Co.

Guessing this situation ain't going away any time soon.

Stay tuned ...