Labour Party legislator Stella Creasy was targeted after she tweeted in support of feminist campaigner Caroline Criado-Perez, who received a torrent of abuse after she campaigned, successfully, for Jane Austen to appear on a British bank note.
The Metropolitan Police said Tuesday it was investigating "an allegation of malicious communications" on Twitter.
The incidents have led to calls for Twitter to take action against abusive commenters, known as trolls.
Twitter said it took the issue seriously and planned to expand a "report abuse" button, already available on its iPhone app, to other platforms.
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