Speaking to the BBC's Chris Mason at the G7 summit in Hiroshima, the prime minister said he was leading the way with new sanctions on Russia.
He said he hoped other countries would follow suit.
Russian diamond imports to the UK are among the items that will be banned by the government.
The Russian diamond industry was worth $4bn (£3.2bn) in exports in 2021.
Russian-origin copper, aluminium and nickel imports will also be blocked, under legislation to be introduced later this year.
"We believe in democracy, freedom, the rule of law - and it's right that we stand up for those things," Mr Sunak told the BBC.
"I'm hopeful and confident that our partner countries will follow as they have done when we've done this previously.
"That will make the sanctions more effective, ensure that Russia pays a price for its illegal activity."
The UK government said it was also planning to target 86 more people and companies connected to President Vladimir Putin, including people who were "actively undermining the impact of existing sanctions".
Since Russia's attack on Ukraine, the UK has targeted more than 1,500 individuals and entities and frozen more than £18bn assets under the sanctions regime.
Last year the UK, US, Canada and Japan banned imports of Russian gold in an effort to hit the country's ability to fund the war in Ukraine.
Downing Street said more than 60% of President Putin's war chest has been "immobilised" - worth about £275bn.
Both the US and the EU have announced similar sanctions on Russia - with US President Joe Biden setting out plans to ban Russian diamonds, seafood and vodka last year.
The President of the European Council, Charles Michel, says the EU also wants to restrict trade in Russian diamonds to try to further isolate Moscow.
Mr Sunak is in Hiroshima for the G7 summit, which is comprised of some of the world's richest nations.
The prime minister will visit the site of the first nuclear bomb detonation at the Hiroshima Peace Park alongside other G7 leaders before the meeting where the Ukraine war and economic security are likely to be high on the agenda.
Russia has significantly increased the frequency of its missile attacks on Ukraine recently, while Ukraine appears to be shooting down more of Russia's missiles.
At the meeting, Mr Sunak is expected to warn other world leaders "against complacency in defending our values and standing up to autocratic regimes".
On Sunday, he will meet the prime minister of India, Narendra Modi, who is attending the G7 summit as a guest.
Mr Modi has remained neutral on Russia's invasion of Ukraine, calling for peaceful dialogue to end the conflict.
Mr Sunak told reporters travelling with him in Japan that he had seen "positive" steps from India in its stance on the war.
The prime minister said the sanctions demonstrated the G7 was unified in the face of the threat from Russia.
He said: "We are meeting today in Hiroshima, a city that exemplifies both the horrors of war and the dividends of peace.
"We must redouble our efforts to defend the values of freedom, democracy and tolerance, both in Ukraine and here in the Indo-Pacific."