The leaders of Germany, France and Italy said there can be no negotiations with Britain on the country's depature from the European Union until London has formally declared its intention to quit.
German Chancellor Angela Merkel said "we agree there will be no formal or informal talks" with Britain until Article 50 has been invoked.
"We will suggest to our (EU) colleagues that we should put in place a new impulse ... in the coming months," she said, adding that areas in which a new push would be made included "defence, growth or jobs and competitiveness".
All three leaders insisted there would be no informal talks about the ins and outs of Brexit until Britain gives formal notice to the EU by invoking Article 50 of the Lisbon Treaty, which would lock the country into a two-year timeline to negotiate its exit.
Merkel has attempted to rein in pressure on London to move quickly.
"We cannot afford a deadlock, ... but I have some understanding for the fact that Britain is taking a certain amount of time to analyse the situation," Merkel said during a press conference earlier Monday.
British Prime Minister David Cameron on Monday repeated an earlier statement that he would leave the decision to initiate Article 50 to his successor, whom he initially said was unlikely to be chosen before his Conservatives' party conference in October.
However, a key party committee said nominations would be taken this week, with plans to have a new leader in place by September.
During the first address to British lawmakers since the country voted to leave the EU on Thursday, Cameron said that Britain would not give formal notice "at this time," as it must first "determine the kind of relationship we want with the EU."
US Secretary of State John Kerry warned the EU against a "revengeful" approach and called on leaders to act in a "responsible, sensitive" and strategic manner.
"I think it is absolutely essential that we stay focused on how, in this transitional period, nobody loses their head, ... people don't start ginning up scatterbrained or revengeful premises," Kerry said during a visit to Brussels.
Renzi, speaking in the Italian Senate before flying to Berlin, said that "the last thing Europe should do is embark on a discussion on procedures for a year."
This week's EU summit should "be about the relaunch" of the European project and "not just about exit procedures" for Britain, Renzi said.
French Foreign Minister Jean-Marc Ayrault said during the weekend that divorce proceedings with the EU should be triggered in the coming days, but Merkel said later that rushing into an exit would be unwarranted.
In an interview with broadcaster France 2, French Finance Minister Michel Sapin said "there is no difference between France and Germany" regarding the timeline for Britain's withdrawal.
"Should Great Britain go quickly? Yes. France, like Germany, says that Britain has voted [and that] Brexit should be implemented starting now," he said.
Merkel, Hollande and Renzi will attend an EU leaders summit in Brussels on Tuesday and Wednesday alongside counterparts from the other remaining 24 EU member states.
The possibility of Britain handing off its EU presidency, due to take place in the second half of 2017, will also be discussed at the summit, EU sources said.