The demands come after it was brought to light that the gunman in the El Paso shooting posted a hate-filled, anti-immigrant manifesto on online message board website "8chan", the screenshot of which went viral on major social media platforms such as Facebook and Twitter.
People believe that while smaller platforms like "8chan" might be the places to promote white supremacist ideas, it is Twitter where these ideas become mainstream.
"22 people in El Paso were killed when a white supremacist said he wanted to kill as many Mexicans as possible, Twitter, you need to take an action. This cannot be promoted on a mass platform," a tweet read.
"Twitter's user-base clearly wants them to ban 8chan. It's a cesspool of hate that incubates white supremacist mass murderers and facilitates child pornography trafficking to boot. Why is 8chan verified? Why is Twitter not taking action on white supremacists post," another tweet said.
US President Donald Trump also took to his Twitter handle and urged social media companies to "develop tools to detect mass shooters before they strike."
Previously, Twitter's senior policy strategist, during a recent Congressional hearing said that the company took action against 184 groups that violated the company's policy on violent extremism.
Earlier in March, Facebook also said it would bar white nationalist and white separatist content from its platform.
( With inputs from IANS )