US Secretary of State Mike Pompeo has told Saudi Arabia's king and crown prince that "every single person responsible" for the murder of Saudi writer Jamal Khashoggi needs to be held accountable.

King Salman and Crown Prince Mohammed bin Salman, also known as MBS, "both acknowledge that this accountability needs to take place", Pompeo said in Riyadh following talks with the two men on Monday.

"They reiterated their commitment to achieving the objective, the expectations we set for them," Pompeo added.

The secretary of state told reporters he had also raised a number of human rights issues with the king and MBS, including women's rights activists who have been detained for months and some allegedly tortured.

Khashoggi, a longtime royal insider who had become a critic of Prince Mohammed, was killed in October in the kingdom's Istanbul consulate, prompting a global outcry, including treasury sanctions on 17 individuals and a US Senate resolution blaming MBS.

US President Donald Trump and Pompeo, however, have so far been reluctant to directly implicate the royal or issue any punitive measures.

A CIA assessment has blamed Prince Mohammed for ordering the killing, which Saudi officials deny.

At least 21 Saudis have been arrested in the case, with five facing the death penalty. Five officials were also fired, including a senior royal adviser.

The outcry over Khashoggi's murder has strained ties with Western allies and focussed attention on Saudi Arabia's domestic crackdown on dissent and the nearly four-year-old war in Yemen.

During meetings that lasted about 80 minutes total, Pompeo said he had spoken with Saudi leaders about women's rights activists arrested last summer and accused of treason.

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"Their commitment was that the lawful judicial process would take place and they would do so quickly, and that they would continue down that path," he told reporters.

'Need for de-escalation'

On Yemen, Pompeo and Prince Mohammed agreed on the need for continued de-escalation and adherence to agreements made last month at talks in Sweden to end the civil war between the Saudi-backed government and the Iranian-aligned Houthis.

"We talked about the fact that work done in Sweden on Yemen was good but we need both sides to honour those commitments. To date, the Iranian-backed Houthis have chosen not to do that," he said.

Pompeo, whose earlier stops included Cairo, Abu Dhabi and Doha, will cut short the rest of his Middle East trip to attend a family funeral, a State Department spokesman said. He will return home after meetings in Oman instead of travelling on to Kuwait.

The tour comes amid conflicts raging in Syria and Yemen, while the US is trying to ensure a unified front against Iran, which it accuses of expanding its political and military footprint in the Middle East.