Theresa May has offered “warm words” on human rights, but no action against Saudi Arabia on the war in Yemen or the killing of a Saudi journalist, Jeremy Corbyn has said, challenging May’s claim to have been “robust” with the Saudi leader at the G20 summit.

Speaking to MPs after returning from the summit in Argentina, May said she had met the Saudi crown prince, Mohammed bin Salman, to discuss both the murder of Jamal Khashoggi and ways to end to the conflict in Yemen, including progress at the upcoming talks in Stockholm.

“Our relationship with Saudi Arabia is important to this country, but that does not prevent us from putting forward robust views on these matters of grave concern,” she said.

Corbyn said May’s comments meant nothing without concrete action. “While economics are important, our belief in universal human rights and democratic principles must never be subservient to them,” he said.

The Labour leader called the Saudi prince “the chief architect of the brutal war in Yemen” and someone “believed to have ordered the murder of Jamal Khashoggi”.

May shook her head as the Labour leader said she had “asked nicely” for him to investigate the murder and not to use the weapons sold by the UK to Saudi Arabia in the war in Yemen.

“Leaders should not just offer warm words against human rights atrocities but back up their words with action,” he said, citing Germany and Norway as countries who have stopped selling weapons to Saudi Arabia, when Britain has not.

During his response to May, Corbyn also said that, 10 years after the financial crash of 2008, G20 leaders had been “too slow to reject the failed neoliberal economic model that caused the crisis”.

Corbyn said the exception was the “mandate for change” won by the new Mexican president, Andrés Manuel López Obrador, whose inauguration he attended this weekend.

In her opening statement, May said the UK had kickstarted discussions on future trade deals with Australia, Japan, Argentina, Chile and Canada at the G20 summit.

“I came with the clear message that Britain is open for business and that we are looking forward to future trade agreements,” she said. “Once we leave the EU, we can and we will strike ambitious trade deals.

“For the first time in more than 40 years, we will have an independent trade policy, and we will continue to be a passionate advocate for the benefits open economies and free markets can bring.”

However, the reaction at the summit was mixed. May met leaders including the Canadian prime minister, Justin Trudeau, the Australian prime minister, Scott Morrison, and the Japanese prime minister, Shinzō Abe, all of whom expressed some scepticism about the state of her Brexit deal.

Abe, whom Downing Street sees as a close ally on Brexit matters, told May to avoid a no-deal Brexit, while Morrison said he knew the prime minister had to deal with “a very tough set of issues”.