The boss of Twitter UK has said sorry to women who have experienced abuse on the social networking site.
Tony Wang said the threats were "simply not acceptable" and pledged to do more to tackle abusive behaviour.
The apology came as Twitter updated its rules and confirmed it would introduce an in-tweet "report abuse" button on all platforms, including desktops.
Police are investigating eight allegations of abuse including bomb and rape threats made against women.
Two people have been arrested in relation to rape threats against Labour MP Stella Creasy and feminist campaigner Caroline Criado-Perez, who received the threats after a campaign to have Jane Austen on the new £10 note.
The Guardian's Hadley Freeman, the Independent's Grace Dent and Time magazine's Catherine Mayer all said they had received identical bomb threats on Wednesday.
The revelations sparked a backlash online, with a petition calling for Twitter to add a "report abuse" button to tweets attracting more than 125,000 signatures so far.
In a series of tweets, Twitter UK general manager Mr Wang said: "I personally apologize to the women who have experienced abuse on Twitter and for what they have gone through.
"The abuse they've received is simply not acceptable. It's not acceptable in the real world, and it's not acceptable on Twitter.
"There is more we can and will be doing to protect our users against abuse. That is our commitment."
Minister for Women and Equalities Jo Swinson said unchecked Twitter abuse had been a problem for a long time and she was "delighted" the company was apologising and taking action.
Ms Mayer, Europe editor of Time magazine, said she had yet to receive a personal apology from Twitter, despite contacting the website on Wednesday evening.
"I've been deeply amused by the phrase I've received a personal apology from Twitter," she said.
"If he [Mr Wang] would like to make an apology to me, he can direct message me if he doesn't want to do it publicly."
She added: "We're not being targeted because we're activists, we're being targeted because we're female."
Ms Creasy said she had received a "very welcome" apology in an email from Mr Wang - but it had taken a week.
She said stalking was taking a new form online and called for a mechanism similar to a panic button system to be put in place.
"We need to get round the table with the police and experts to identify the best way we can keep people safe online," she said.
In an earlier message posted on the Twitter UK blog, the company's senior director for trust and safety, Del Harvey, and Mr Wang, said the company had clarified its anti-harassment policy in light of feedback from customers.
They said: "It comes down to this: people deserve to feel safe on Twitter."
Twitter has clarified its guidance on abuse and spam - reiterating that users "may not engage in targeted abuse or harassment".
The "report abuse" button already available on the iOS Twitter app and mobile site will also be rolled out to the main website and Android app from September, Twitter said.
The bosses said in the blog that additional staff were being added to the teams that handle reports of abuse and the company was working with the UK Safer Internet Centre, which promotes the safe and responsible use of technology.
"We are committed to making Twitter a safe place for our users," they said, adding: "We're here, and we're listening to you."
Ms Criado-Perez, 29, welcomed Twitter's response but said the process for reporting abuse should be further simplified to take the onus off the victim.
She said: "Twitter's 'report abuse' button on the iPhone application goes through to the old reporting form. What we're looking for is an overhaul of the system which sits behind the button.
"Right now, all the emphasis is on the victim, often under intense pressure, to report rather than for Twitter to track down the perpetrator and stop them."