Shadow justice secretary David Lammy has called on Twitter to be "faster at stamping out racist threats" after receiving abuse online.
The black Labour MP reported a user to the Metropolitan Police on Sunday after getting a tweet using a racial slur and saying he would "hang from a lamppost".
But the user's account wasn't suspended until Monday, after further tweets from Mr Lammy highlighting the abuse.
Twitter said racist behaviour had "no place on our service". A spokesman for the company said it had suspended the account for violating its hateful conduct policy.
But Home Secretary Priti Patel called for Twitter to take "decisive action" faster in such cases.
Labour leader Sir Keir Starmer also condemned the abuse, saying: "Social media platforms must be quicker at taking action against hate. Racism has no place online or anywhere in our society."
The Metropolitan Police confirmed it had received "an allegation of malicious communication", adding: "The contents are being assessed."
The incident comes after the social media company was criticised for taking too long to act over anti-Semitic tweets by British grime star Wiley.
After Mr Lammy received the tweet on Sunday, calling him a "monkey boy", he posted: "Vile racists like you will not silence me. But social media must not be a platform for threats and abuse."
After 13 hours, he tweeted the abuse again, saying the police were investigating but Twitter had not taken any action.
"You need to get so much faster at removing hate," the Labour MP wrote.
Ms Patel replied to him, condemning the abuse, and saying she had asked the force to keep her updated on its investigation.
She added: "As I have said before, Twitter must take decisive action against this sort of vile content much faster."
Mr Lammy said: "Cross-party consensus can feel rare in British politics. But Twitter, we are united on this."
Other MPs have also tweeted their support for Mr Lammy.
Shadow home secretary Nick-Thomas Symonds wrote: "This abuse is absolutely unacceptable. It's right that the police look into this and clear that social media companies need to do far more.
"Although, knowing David as I do, anyone who thinks they can silence him with vile racism couldn't be more wrong."
A Twitter spokesman said: "We have policies in place that address abuse and harassment, violent threats, and hateful conduct.
"If we identify accounts that violate any of these rules, we'll take enforcement action."