Labour MP Angela Rayner has said she recently received rape and death threats from “someone claiming to be a Jeremy Corbyn supporter” and that she had had panic buttons fitted at her home.

The shadow education secretary spoke out about her experience on Monday after receiving a string of “nasty tweets and social media comments”, after she had praised Tony Blair’s performance in a Sunday television interview.

Rayner said that the abuse she had received “proves we have a problem with some on the left that cannot disagree respectfully” in a Facebook posting. “We have to stop the personal attacks and be kinder to each other,” she wrote.

The MP added: “It was only a couple of weeks ago someone claiming to be a Jeremy Corbyn supporter was arrested for making threats to rape and murder me on social media. My house has panic buttons fitted.”

Labour and some of its MPs have been embroiled in an increasingly intense series of disputes over the last fortnight, at a time when there have been further complaints about antisemitic and other bullying incidents both online and in person.

Corbyn himself was hit on Sunday as he came out of a mosque he had been visiting. A man from north London was charged with assault following the incident, having allegedly screamed: “When you vote, you get what you vote for.”

Several Labour MPs have voiced concerns about their safety, complaining about what they say is a growing level of personal threats. High in the memory of the party’s MPs is that Jo Cox was murdered in 2016 while on her way to a surgery in her Yorkshire constituency.

On Sunday, Rayner had tweeted she had seen “one of the best interviews I’ve seen from Tony Blair” on the BBC’s Andrew Marr show, and said “all shades of red are needed in our Labour party to take on this nasty Tory government”.

That unleashed a string of online criticism, some of which Rayner later reproduced, including one reply that described the MP as a “a war criminal, Tory enabling, TIG [The Independent Group] donating Blair supporter.” Another said: “All shades of red!!! Fuck off.”

Rayner sought to clarify her position on Monday, writing: “I respect Tony’s right to disagree as did Jeremy when Tony was leader. I’m glad he isn’t leaving the party. We need more members not less. We have to unite as a party.”