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EU leaders to meet without Cameron after Brexit vote
Tuesday's meeting in Brussels was Mr Cameron's final EU summit, after he announced his intention to stand down by October.
The 27 other leaders will shortly gather in the Belgian capital to discuss the future without the UK. This has not happened for more than 40 years.
The BBC's Chris Morris in Brussels says there will be calls for unity and for reform, and promises will need to be put into practice quickly because the UK referendum has shaken Europe to the core.
On Tuesday, Mr Cameron said the rest of the EU wanted to have the "closest possible" relationship with the UK after Brexit.
But he said immigration was a "great concern" among UK voters and squaring this with access to the EU single market would be a "huge challenge".
In Brussels, German politicians insisted the UK cannot "cherry-pick" aspects of the EU.
Mrs Merkel stressed that the UK must accept free movement if it wanted to retain access to the single market.
"We all regretted the result and made clear that the legal procedure must be that the UK invokes Article 50," she said. "Mr Cameron said he would hand it over to the new government to do. We all agreed that before that point, there can be no formal or informal negotiations."
She added: "We can see no way to turn this around. It's not a time for wishful thinking, but of contemplating the reality."
European Commission President Jean-Claude Juncker said the UK did not have "months to meditate" on activating Article 50.
"If someone from the Remain camp will become British prime minister, this has to be done in two weeks after his appointment," he said.
"If the next British PM is coming from the Leave campaign, it should be done the day after his appointment."
Mr Cameron told reporters the discussions had been "calm, constructive and purposeful".
He said there was "universal respect" for the UK's decision to leave despite a "tone of sadness and regret".
While the EU wanted more information about the UK's negotiating plans going forward and a "clear model appearing", he said there was an acknowledgement that this would take some time and "no great clamour" for talks to begin straight away.