Kobe Bryant Saves the Day After Cops were Called to Book Signing

All hell ALMOST broke loose at a Kobe Bryant book signing in L.A. on Tuesday -- with cops responding to an upset crowd ... but sources at the scene tell us Mamba stepped in and diffused the situation.

Kobe was set to meet with 500 fans at Barnes & Noble at The Grove shopping center -- taking pictures and signing copies of his new book, "The Mamba Mentality: How I Play."

We're told everything was going fine until someone at the store let in an additional 300 people with less than 30 minutes left in the event.

When time was up and Kobe had to leave, sources say the crowd became upset -- and cops responded to keep the peace.

The good news -- one witness tells us Kobe grabbed the mic, thanked everyone for coming and said he would stay late until he met every person who came out to the event.