“We don’t agree with this and repeat that Russia had absolutely nothing to do with the Skripal case,” he said.

Sergei Zheleznyak, a lawmaker from the United Russia party, said that the European Union, under pressure from London and Washington, “was forced to concoct a statement that is vague in content and politicized in essence.”

The declaration was a somewhat surprising success for Mrs. May, who has often found herself at odds with her European counterparts as she negotiates Britain’s exit from the bloc, a process known as Brexit. The text was tougher than one agreed to earlier this week by European Union foreign ministers after talks attended by Britain’s foreign secretary, Boris Johnson.

The issue of relations with Russia divides European Union nations sharply, and there has been pressure from some to lift economic sanctions against Moscow, so Britain has not pressed for additional steps of that kind. However the Irish Prime Minister, Leo Varadkar, said there was talk of the existing measures being renewed for a 12-month period; currently they have to be rolled over every six months. In any event, the Skripal case has reduced prospects of them being relaxed anytime soon.

Before the summit meeting, Mr. Putin spoke by phone with three European Union leaders, the Kremlin announced, a reminder that Moscow has allies within the bloc.

Several countries, including Cyprus and Greece, have close ties to the Kremlin and have been reluctant to take a tougher line. But in traditional European Union style, they agreed to the latest text after extracting concessions on other issues — in this case, wording critical of Turkey’s actions in the Eastern Mediterranean and the Aegean, the site of tensions over drilling for gas.

Though the European Union’s show of support for Britain is so far largely symbolic, it suggests that even after Brexit, London could retain close ties to the bloc on foreign policy, security and defense. It also underscored the strength of Anglo-French cooperation on such issues, with France taking the lead in pushing for a tough, Europe-wide, response. Mr. Macron said that in the poisoning case the French had been asked for “technical cooperation” by the British, and had reached similar conclusions about Russian culpability.