The European Commission President has urged the US under President Joe Biden to work with Brussels on regulating the tech giants.
"Together, we could create a digital economy rulebook that is valid worldwide: from data protection and privacy to the security of critical infrastructure," Ursula von der Leyen said in a videolink address to the World Economic Forum.
"A body of rules based on our values: Human rights and pluralism, inclusion and the protection of privacy," she said.
The EU in December unveiled landmark draft legislation aimed at curbing the power of the internet behemoths that could shake up the way Silicon Valley can operate in the 27-nation bloc.
The move comes as big tech companies are facing increasing scrutiny around the globe, including in the US, where Google and Facebook are facing competition suits.
Regulators worldwide are pushing to rein in the ability of firms to dominate markets and are pushing to make them more accountable for content published online.
"The business model of online platforms has an impact not only on free and fair competition, but also on our democracies, our security and on the quality of our information," von der Leyen said.
"That is why we need to contain this immense power of the big digital companies."
She said the storming of the Capitol in the US highlighted "the darker sides of the digital world" in spreading hate speech and misinformation.
But she insisted there should be legislation governing issues of free speech online and that those choices should be not left to the tech firms.
"No matter how tempting it may have been for Twitter to switch off President Trump's account, such serious interference with freedom of expression should not be based on company rules alone," the EU chief said.
"There needs to be a framework of laws for such far-reaching decisions," she added.
Ursula von der Leyen also said the European Union will seek to create a bio-defence preparedness programme in the form of a public-private partnership, to prepare against the next big health crisis.
The 27-nation bloc, like the rest of the world, is struggling to overcome the Covid-19 pandemic that has already killed tens of thousands and prompted economic lockdowns across Europe.
"Europe will propose to create a bio-defence preparedness programme. This will be a public-private partnership," she said at the World Economic Forum's virtual summit today.
Von der Leyen said the programme would seek to prepare the EU before the next pandemic hits by seeking to discover and prepare for known and emerging pathogens, and then developing and manufacturing vaccines at scale to respond to them.
The scheme would secure long-term and predictable funding and bring together cutting-edge tech-companies and blue-chip manufacturers.
It would also include regulators such as the European Medicines Agencies and the European Commission.
"We know that preparedness is everything. And we know that in a pandemic there is no time to lose. We need this new public-private approach to detect earlier, develop together and manufacture faster at scale," von der Leyen said.
The European Commission President also today called for a global agreement on protecting biodiversity with the same scale and ambition as the Paris climate pact.
Addressing the World Economic Forum by videolink, von der Leyen said the EU would lobby for such a deal at the COP-15 UN biodiversity summit in Kunming, China expected to take place later this year.
"This will have to be like COP21 was for climate, because we need a Paris-style agreement for biodiversity," she said.
The Kunming summit was postponed last year due to the coronavirus epidemic, and world governments are focused on fighting the outbreak and restarting their economies.
But von der Leyen, herself a trained doctor before becoming a German politician, said protecting a diverse range of species and habitats could be key to protecting human health.
"If we don't urgently act to protect our nature, the next pandemic will be around the corner," she said, citing an anecdote that suggested deforestation in Africa had displaced bats and contributed to an Ebola outbreak.
"To those who prefer the business case, here it is: More than half of global GDP is dependent on high-functioning biodiversity and ecosystem services - from food to tourism," she said.
The World Economic Forum is an annual get-together of political and business leaders, traditionally held in the Swiss resort of Davos, but this year held online.
Von der Leyen hailed new US President Joe Biden's early decision to return to the 2016 Paris Climate Agreement, which his predecessor Donald Trump had abandoned.