"We are calling on social media companies to do whatever is necessary to prevent the spread of terrorist material on the internet", Tusk added.
Afterward, the 27 other leaders will meet without May to assess the issue themselves.
"Within three months, Member States will agree a common list of criteria and commitments, together with concrete capability projects, in order to take this cooperation off the ground", Tusk said.
"So who knows? You may say I am a dreamer but I'm not the only one", Tusk continued, quoting a lyric from the late John Lennon's "Imagine". There may be sticking points with Brussels, such as the cut-off date for European Union citizens in Britain to retain rights under the bloc's free movement rules and European Union demands to preserve a panoply of rights in the future that may irk those keen to reduce immigrant numbers.
Almost two decades after France and Britain, the EU's main military powers, helped form a common European foreign policy, the continent faces a growing range of security threats, from Islamic State militants to a more assertive, hostile Russian Federation that has seized territory in Ukraine.
Belgian Prime Minister Charles Michel has immediately countered the suggestion of European Council President Donald Tusk that the door for Britain to stay in the EU is still slightly ajar.
Michel wrote in a Twitter message: "It's time for action and certainty. I don't think that May will want to shatter that understanding", said one European Union diplomatic source, who asked not to named.
Theresa May has played her opening gambit of Brexit negotiations, telling European leaders she will offer some three million EU citizens a new "settled status" allowing them to stay in Britain if they have lived here five years. "European countries that don't respect the rules have to draw all the political consequences", Macron said in an interview with eight European newspapers ahead of the summit. "President Dalia Grybauskaite of Lithuania, which has over 100,000 citizens in Britain, insisted relations would remain close and tweeted the Motown lyric: "#Brexit: "ain't no mountain high enough". Downing Street declined to comment.
May is going to Brussels for her first European summit since losing her Parliament majority in the election earlier this month.
She seemed keen to calm the mood with the continentals after weeks of sniping during her election campaign, describing the first formal meeting of Brexit negotiators on Monday as "very constructive" and stressing that London wanted a "special and deep partnership with our friends and allies in Europe".
Tusk has made the comments a few hours before a bilateral meeting with British Prime Minister Theresa May.
Speaking over dinner at the Brussels summit, Mrs May told leaders of the other 27 European Union nations: "The UK's position represents a fair and serious offer and one aimed at giving as much certainty as possible to citizens who have settled in the UK, building careers and lives and contributing so much to our society".
Quoting John Lennon, he said that when people asked him if he thought there was any possibility of the United Kingdom remaining a member, he replied: "The European Union was built on dreams that seemed impossible to achieve".
"We are witnessing the return of the European Union rather as a solution, not a problem", he wrote.