10:56 AM PT -- Evander Kane and his attorney have issued a statement adamantly denying the allegations in the suit.

"We’ve received notice of the filing of a lawsuit by someone referred to as Jane Doe alleging a breach of contract against Evander Kane," the statement reads.

"We firmly believe that this lawsuit is baseless both factually and legally. We will aggressively defend this claim in court on Evander’s behalf and assert all applicable counterclaims."

NHL superstar Evander Kane is being sued by a woman who claims he promised to pay her $3 MILLION to abort their child ... so she did ... but he never ponied up the dough.

It's all in a lawsuit filed by a woman using the alias "Jane Doe" to protect her identity. In the suit, the woman claims she started dating Kane in 2015.

Doe claims Kane got her pregnant in 2016 -- but they both agreed to get an abortion.

They continued to have a sexual relationship and he knocked her up again in 2017. Doe claims Kane pressured her to abort again because a baby would damage his hockey career ... and also ruin the relationship he had with his official "girlfriend."

The woman ultimately agreed to a 2nd abortion.

Then in May 2018, Doe claims Kane got her pregnant for a 3rd time -- even though she had used Plan B as a last-ditch attempt at birth control.

But, this time, Doe claims she did not want to abort -- which caused problems with Kane.

In her suit, Doe claims Kane told her proceeding with the pregnancy would be a "huge mistake" so he started "bullying" her into seeking a 3rd abortion.

When she refused, Doe claims Kane offered her $1 million to change her mind. She told him no. So, Kane came back with a $3 million offer ... and it was an offer Doe admits she couldn't refuse.

Doe claims she had the abortion in June 2018 -- but Kane never made good on the $3 million payment.

When she followed up with him, Doe claims Kane strung her along ... until finally telling her he wasn't going to make the payment.

She claims Kane tried to turn the tables and accused her of extortion -- and ultimately instructed her to solely deal with his attorney.

The woman is suing for more than $6 MILLION for the $3 million payment -- AND other damages including intentional infliction of emotional distress.

We've reached out to Kane's attorney for comment -- so far, no word back.

27-year-old Kane is one of the best hockey players in the NHL -- and recently signed a 7-year, $49 million contract extension.

Kane was the 4th overall pick in the 2009 NHL Draft and went on to score 190 goals in his career ever since.