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The 42-year-old singer initially shared a post on Instagram on Sunday, saying she was sorry if she had "offended any of the people I genuinely care about" in her memoir, The Woman In Me.
The book, published in October, revealed she had an abortion while dating the former NSYNC star.
Spears posted the apology along with a clip of Justin Timberlake singing on Saturday Night Live, and added: "I also wanted to say I am in love with Justin Timberlake's new song 'Selfish'. It is soo good and how come every time I see Justin and Jimmy together I laugh so hard?"
She has since deleted the apology and accompanying posts after Timberlake appeared to respond during his concert in New York on Wednesday.
In a video recorded during his performance at the Irving Plaza, Timberlake could be heard telling the crowd: "I'd like to take this opportunity to apologise to absolutely f****** nobody."
Spears deleted her apology and then appeared to respond to Timberlake in another message on Thursday.
It read: "Someone told me someone was talking s*** about me on the streets!!! Do you want to bring it to the court or will you go home crying to your mom like you did last time??? I'm not sorry!!!"
Spears was 17 when she began dating Timberlake in 1999 after they met on the Mickey Mouse Club, which was a launchpad for numerous celebrities including Christina Aguilera and Ryan Gosling.
The pair were together until 2002.
Read more: Ten revelations from Britney's tell-all book
In her memoir, Spears described the unplanned pregnancy as a "surprise".
She wrote: "For me, it wasn't a tragedy. But Justin definitely wasn't happy about the pregnancy. He said we weren't ready to have a baby in our lives, that we were way too young.
"If it had been left up to me alone, I never would have done it."
She also described the abortion as "one of the most agonising things I have ever experienced in my life".
Timberlake's response has triggered backlash on social media from many Spears fans, some of whom have attempted to get the hashtag "#canceljustintimberlake" trending.