The rapper claims he and Emily have not split, and insists they're a "couple working on our relationship." He adds that the mystery woman he was seen with at a Mexican restaurant last week was not a date ... rather a lunch meeting with a teacher.

Fabolous says he loves Emily B and our story is baseless. He's also threatening legal action for defamation.

Here's the thing -- sources close to Emily tell us the 2 haven't been together for nearly a year ... and it was her decision to call it off. Despite Fab's claims they're still trying to work it out -- we're told, for now, Emily says it's over -- and Fab is trying to save his family.

Emily's recent post on her Instagram Story seems to bear this out. She says this year's all about prioritizing mental health over relationships. According to the post, Em's mindset is ... "I'll lose anyone and anything before I lost my mind."

As you know ... they had major issues, especially after video surfaced of Fabolous' physical altercation with Emily in March 2018. He was indicted for domestic violence in October, but struck a plea deal early this year to avoid jail time.