A rapid response unit to combat hostile state action ranging from cyber-attacks to poisonings has been agreed by G7 members meeting in Québec.

The launch of the initiative, which has been led by Theresa May, was at odds with Donald Trump’s call to readmit Russia to the G7. May said her view on dealing with Russia was to “engage but beware”.

“We should remind ourselves why the G8 became the G7 – it was because Russia illegally annexed Crimea,” she said. “We have seen malign activity from Russia in a whole variety of ways, of course including on the streets of Salisbury in the UK.

“So we need to say, I think, before any such conversations can take place, Russia needs to change its approach.”

Downing Street sources indicated later that although there were points of difference between May and Trump, the president had been robust in attributing blame for Russia’s hostile actions in the US and the UK.

May discussed details of the proposals for the rapid response unit in bilateral meetings with France’s Emmanuel Macron and Germany’s Angela Merkel as the G7 summit got under way.

The plans amount to a formalisation of the response that May worked hard to achieve after the Russian former spy Sergei Skripal was targeted in an assassination attempt in Salisbury in March.

May persuaded more than 20 allies to expel Russian diplomats, although the response varied significantly – the US expelled 40, Germany just four. The patchy response reflected May’s struggle to build a united front against Russia.

One of the objectives of the initiative is described as “improving understanding of partner countries’ polices and thresholds for taking action”.

May said the announcement in Québec showed the G7 was united in its intolerance of foreign interference. “We are getting organised, and … we will take coordinated action against those who seek to violate the rules based international system,” she said.

The proposals include greater sharing of intelligence around potential threats and techniques to combat them.

May said calling out such activity would “help to end hostile states’ false sense of impunity, demonstrate our awareness of their activity and underline our unwavering willingness to defend ourselves”.

More coordinated action with the Organisation for the Prohibition of Chemical Weapons, which spearheaded the independent investigation into the Skripal poisoning, is planned. There will be a meeting in London in the coming weeks to consider ways of strengthening the OPCW’s role.

May has called for more cooperation to understand and detect illicit money flows and to agree on concrete action “to stop dirty money undermining our democracies”.

Last month the cross-party foreign affairs committee of MPs said the government was putting national security at risk by allowing “kleptocrats and human rights abusers to use the City of London to launder their ill-gotten funds to circumvent sanctions”.

The MPs said that despite May’s rhetoric in the wake of the Skripal affair, nothing had changed. “These assets, on which the Kremlin can call at any time, both directly and indirectly support President Putin’s campaign to subvert the international rules-based system, undermine our allies and erode the mutually reinforcing international networks that support UK foreign policy.”

On the day the report was published in May, it emerged that the Chelsea owner Roman Abramovich, regarded as a close Putin ally, had not had his visa renewed. He has since put on hold plans for £1bn investment in the football club’s new stadium, and the future of his ownership of Chelsea is thought to be in doubt.

But with Trump calling for Russia to be readmitted to the G7, from which it was suspended after the Crimea invasion, and the new Italian government questioning sanctions against Russia, there is still a rough road ahead for May’s plans. They will come up at a bilateral meeting between May and the Italian prime minister, Giuseppe Conti, on the margins of the G7 summit.