Sir Keir Starmer is demanding urgent government action to "clean out the cesspit" of online extremism.
The Labour leader offered to work with Prime Minister Boris Johnson to fast track new online safety laws.
Mr Johnson promised to get the first stage of the long-awaited Online Safety Bill through the Commons by Christmas.
He said it would include criminal sanctions for those allowing "foul content" - but did not confirm whether that would include company directors.
Labour is calling for the directors of internet firms to be held liable for the content of messages posted on their sites.
Speaking at Prime Minister's Questions, Sir Keir said it was now three years since the government had promised a crackdown on online extremism and hate speech but the proposals had yet to begin their passage into law.
"Meanwhile, the damage caused by harmful content online is worse than ever," he told MPs.
He criticised "dangerous algorithms" on Facebook and Instagram - and said he had been shown examples of "violent Islamism and far-right propaganda" on TikTok, a social media site popular with teenagers.
But he added: "Telegram has been described as the app of choice for extremists."
Power to fine
Telegram, which has half-a-billion users, is a messaging app, which also has "channels" allowing individuals to broadcast to an unlimited audience.
Telegram has risen to global prominence as an app of choice to co-ordinate global protest movements; but has also been accused of not doing enough to purge extremist channels run by those involved with the so-called Islamic State group and the Capitol Hill riots.
Campaign group Hope Not Hate and the Board of Deputies of British Jews had both said the free-to-use encrypted messaging service had "facilitated and nurtured a sub-culture that cheerleads terrorists", Sir Keir said.
The messages shown to Sir Keir by Hope Not Hate, posted by anonymous Telegram users, include threats to "kill all women", "kill politicians" as well as homophobic, Islamophobic and racist abuse.
Sir Keir said "tough sanctions" were needed - but the government's proposed legislation did not include criminal sanctions against the directors of online platforms.
Mr Johnson said the government would look at ways to "toughen up" the law and promised to "come down hard on those who irresponsibly allow dangerous and extremist content to permeate the internet".
He added: "What we hope for also, is that no matter how tough the proposals we produce, that the opposition will support it."
Regulator Ofcom would have the power to levy fines of up to £18m or 10% of global profits, whichever is higher, on social media platforms which fail to comply with the new online safety laws.
The regulator would also be given the power to block services from the UK if they are deemed to present a risk of significant harm to UK citizens.
The bill also includes an option to introduce a new criminal offence for senior managers if further action is needed to ensure compliance - something Labour has been calling for.
Asked if Mr Johnson was now backing criminal sanctions, a Downing Street spokesperson said the government was "alive" to the issue, adding: "We will continue to listen and work with the companies involved."
Conservative MP and chairman of the Department for Culture, Media and Sport committee Julian Knight said a quicker timetable for the bill risked undermining scrutiny of it.
"We find ourselves in an unworkable situation where, at the whim of the prime minister at the despatch box, the process of scrutiny of this important piece of legislation to tackle online harms will be undermined. We need urgent clarity on this matter," said Mr Knight.
Is messaging app Telegram a haven for extremists?
By Alistair Coleman, BBC Monitoring
Labour Leader Sir Keir Starmer claimed that the messaging app Telegram is "the app of choice" for extremists. But is he right?
Extremist content has been largely forced off mainstream social media platforms like Facebook, Instagram and Twitter, and terror groups have moved elsewhere in attempts to spread their ideologies.
Telegram has half a billion users, the vast majority using the service in the way it was designed - to exchange messages, images and video with friends, family, and people with shared interests.
In countries like Iran, it's one of the few platforms where people can speak freely about social issues and politics without fear of persecution.
However, there are significant numbers who use Telegram to share extremist content and illegal pornography.
Attracted by the platform's secret chats with end-to-end encryption and its seemingly relaxed content moderation policies, Telegram became a haven for jihadist groups, earning it the name "Terrorgram". Working with international law enforcement agencies, Telegram has been successful in eliminating most jihadist content.
But other extreme content, including what might be defined as "terrorist" is still present. It's easy to find racism, sexist and homophobic abuse, anti-Semitism, neo-Nazism, violent imagery, and encouragement of criminal activity on Telegram from users in the UK and around the world.
Telegram told the BBC that it was "surprised" by Sir Keir's statement, saying that "calls for violence are expressly forbidden on Telegram".
"Our moderators routinely remove content that violates this rule using a combination of proactive monitoring of public spaces and user reports," the Telegram statement concluded.