The actor and activist Rose McGowan has issued an apology to Asia Argento after the latter threatened legal action over what she termed “horrendous lies” in connection with sexual assault allegations made against Argento by the actor Jimmy Bennett.

In a statement posted on Twitter, McGowan said an earlier statement she had made about the allegations “contained a number of facts that were not correct” and that she “deeply regret[ted] not correcting my mistake sooner and apologise to Asia for not doing so”.

McGowan said that her most “serious” mistake was to allege that Bennett had sent explicit text messages to Argento when he was 12 years old and that Argento had not acted appropriately on receiving them. McGowan said she had “misunderstood the messages that Asia exchanged with my partner Rain Dove”.

Argento had on 17 September given McGowan 24 hours to apologise before, the following day, saying she had instructed lawyers Mishcon de Reya to “seek substantial damages for deception, fraud, coercion and libel”. However, Argento appears to have accepted McGowan’s apology, posting a message on Twitter in response reading: “Although I am grateful to @rosemcgowan for her full apology following her groundless allegations about me, if she had issued it earlier, I may have kept my job on X-Factor and avoided the constant accusations of paedophilia which I have been subjected to in real-life and online.”

Argento then followed it up by posting: “Now go on, live your life and stop hurting other people, will you Rose? Best wishes.”

The confrontation between two prominent figures in the Harvey Weinstein scandal arose after Argento was accused of sexual assault by actor Jimmy Bennett in a New York Times article in August. Bennett claimed she had paid him $380,000 (£290,000) to keep the accusation quiet. Argento has denied the assault allegation, and claims her then partner Anthony Bourdain paid the money to Bennett to help him with “severe economic problems”.

McGowan first responded to the Argento accusation on 20 August, writing “my heart is broken”. Her statement to which Argento refers was issued seven days later.

Police in Los Angeles are investigating Bennett’s claim after it emerged no report to police had been made at the time of the alleged assault in 2013. Argento and Bennett had met after working together on The Heart Is Deceitful Above All Things, her 2004 adaptation of the JT LeRoy novel.