1/10/18 -- Simmons tells us, "I vehemently deny all these allegations. These horrific accusations have shocked me to my core. I am blessed to have shared extraordinary relationships, whether through work or love, with many great women; and I have enormous respect for the women's movement worldwide and their struggle for respect, dignity, equality and power."

He continues, "I am devastated by any reason I may have given anyone to say or think of me in the ways that are currently being described. The presumption of innocent until proven guilty must not be replaced by 'Guilty by Accusation.'"

Russell Simmons has 2 more rape allegations to deal with, because we've learned 2 women have gone to police and filed criminal complaints ... TMZ has learned.

Law enforcement sources tell us the two women filed police reports with the NYPD late last month, alleging the music mogul raped them in 1983 and 1991, respectively.

One of those women is Sherri Hines, who appeared on Megyn Kelly's show in December. She told cops Simmons raped her at his office in '83 ... which jibes with what she said on the show.

The other woman -- who remains anonymous -- claims Simmons raped her at his Manhattan residence after they'd gone out on a date in '91. She was 32 at the time, and alleges he tried taking off her dress while sitting on a couch, and then pushed her down and forcibly raped her when she rejected his advances.

The total number of women accusing Simmons of sexual misconduct was 13 -- the anonymous woman makes it 14. Russell has denied all previous claims against him -- and, as we've reported, he even took and passed a polygraph in an attempt to refute at least one of the allegations.

The NYPD is already investigating Simmons for at least 7 claims of sexual misconduct.