Speaking to The Independent ahead of Twitter's 10th birthday, Mr Daisley said more effort had been put into user safety than any other issue.
"The measures we've taken correlate directly with a reduction in the amount of bad behaviour," he said.
A series of high-profile users have quit Twitter, citing online abuse.
The newspaper reports that the site has been targeting suspected so-called internet trolls - people who use social media accounts to abuse others - by asking more users that they identify themselves through phone verification.
"That allows us to tell the user that what they do here exists in the real world," Mr Daisley told the paper.
The implementation of phone verification - where the user is sent a numeric code they have to enter before accessing the site - also allows Twitter to check if a member has other accounts which have been suspended as a result of abuse, Mr Daisley said.
Users have also been given new tools to block trolls and they have been encouraged to share their lists of blocked accounts, the newspaper reported.
Mr Daisley said the measures had made people feel safer.
In February Twitter's then-chief executive Dick Costolo admitted the company "sucks" when it comes to dealing with abuse and trolling on the service.
The daughter of actor Robin Williams signed off Twitter saying she had been abused by other users after his death.
And Sara Payne, whose daughter Sarah was abducted and murdered in 2000, said she was leaving the social media network after years of online harassment.