Western leaders led by the EU’s Donald Tusk have rejected Vladimir Putin’s claims that liberalism is “obsolete” as they rallied to defend democratic values over oligarchic rule.

The European council president, a well-known critic of Putin’s regime, was the most outspoken in his response to the Russian president’s comments in an interview with the Financial Times.

Tusk, a former prime minister of Poland who was briefly imprisoned for his role in the anti-communist Solidarity movement, contrasted the principles underpinning liberal democracies with rule through “personality cults”.

Speaking at the G20 summit in Osaka, Japan, Tusk said: “I have to say that I strongly disagree with the main argument that liberalism is obsolete. We are here as Europeans also to firmly and univocally defend and promote liberal democracy.

“Whoever claims that liberal democracy is obsolete also claims that freedoms are obsolete, that the rule of law is obsolete and that human rights are obsolete.

“For us in Europe, these are and will remain essential and vibrant values. What I find really obsolete are authoritarianism, personality cults, the rule of oligarchs. Even if sometimes they may seem effective.”

Putin had used a 90-minute interview with the FT to claim “the liberal idea” had “outlived its purpose”, and the public had turned their back on social tolerance, multiculturalism and immigration.

Putin claimed migrants in western democracies had been allowed to “kill, plunder and rape with impunity”. He also appeared to criticise the social tolerance of liberal societies. “They claim now that children can play five or six gender roles,” Putin told the newspaper. “I cannot even say exactly what genders these are. I have no notion. Let everyone be happy, we have no problem with that.”

The absence of any comment from the US president, Donald Trump, about Putin’s claims was notable.

But a spokesman for Theresa May said she had challenged Putin’s attack on the liberal order at a frosty private meeting. The British prime minister also publicly condemned Russia for the use by its intelligence services of novichok nerve agent in Salisbury.

Downing Street said May had told Putin that “the UK would continue to unequivocally defend liberal democracy and protect the human rights and equality of all groups, including LGBT people”.

Boris Johnson told a Conservative leadership hustings that Putin was “totally wrong”, and said he had failed in his ambition of forging a new relationship with Russia when foreign secretary. “I went to Moscow in defiance of a lot of advice. I tried to build a new friendship and a new partnership and it just isn’t there,” he said in Exeter.

“All this stuff Putin comes up with about ‘liberalism is over’ is wrong. He is totally wrong. Our values – freedom, democracy, free speech – those things are imperishable and they will succeed.”

The European commission president, Jean-Claude Juncker, also restated the EU’s commitment to a “rules-based order”.

Latvia’s defence minister, Artis Pabriks, used an interview with Euronews to call on all western leaders to recognise the threat posed by the Kremlin.

He said: “Being a border country, we have been facing Russian airplanes, Russian ships next to our border, daily.

“As they are coming very close, they have different interferences. Of course, they are also interfering from time to time, as far as political events happening in our country, let’s say support for some political forces, political parties …

“And this, what is happening in the Baltics, in Latvia, you can consider as a litmus test for Russian hybrid [inaudible] against many other western nations, as far as the elections in the US or in France, or Brexit, or other places, or elections to the European parliament, because their purpose, in general, is to create larger influence in global world by diminishing [the] power of [the] opponent.”