Saudi Arabia should hold to account “every single person” responsible for killing the dissident journalist Jamal Khashoggi, Mike Pompeo has said in Riyadh.

The US secretary of state refused to be drawn on whether that included his Saudi host, Crown Prince Mohammed bin Salman, whom the CIA has said probably ordered the murder last October.

Pompeo said on Monday he had discussed Khashoggi’s death with the Saudi heir and his father, King Salman, and raised the fate of jailed women’s rights activists. Both issues have buffeted bilateral ties in the three months since the Washington Post columnist was killed. His death left the US scrambling to provide cover for the kingdom, which had been a bedrock of its foreign policy throughout Donald Trump’s first two years in office.

Pompeo’s nine-country tour of the Middle East had been designed to reassure allies of the Trump administration’s commitment to the region in the aftermath of Khashoggi’s death and the furore surrounding the president’s surprise decision to withdraw from Syria.

He had earlier spoken of the US being a regional “force for good” and of his visit marking a “real new beginning” in US policy – a swipe at Trump’s predecessor Barack Obama, whose 2009 address in Cairo, where Pompeo spoke on Thursday, had set the tone for his administration’s regional stance.

“We spoke about human rights issues here in Saudi Arabia, women activists,” Pompeo said. “We spoke about the accountability and the expectations that we have. The Saudis are friends and when friends have conversations you tell them what your expectations are. Every single person who has responsibility for the murder of Jamal Khashoggi needs to be held accountable.”

Pompeo’s tour had taken him to countries increasingly wary of the Trump administration’s stance towards the region, and uncertain about how to deal with a president many felt to be capricious and unwilling to engage outside a narrow band of interests – a significant change from previous Republican leaders, particularly George W Bush, who had tried to impose US values through war and occupation.

Considered to be one of the last “grownups” to have Trump’s ear, Pompeo’s credentials as an Iran hawk are well established. But his readiness to take on Tehran surprised some regional officials, as did his insistence that the US could do so while at the same time withdrawing its ground forces from the border with Iraq and Syria.

As the remnants of Islamic State melt back into the Iraqi deserts, Iran is consolidating areas over which it took control during the almost completed US-led rout of the terror group. US-raised proxies in Syria’s north-east, primarily Kurdish groups, are feeling increasingly exposed as the withdrawal begins.

Many Kurdish leaders believe their interests are being sold out to the US’s Nato ally Turkey, which has threatened to invade the region, with the aim of pushing away Kurdish militants from its border.

Trump muddied the waters further on Sunday when he tweeted that Turkey would face economic consequences if it attacked Kurdish fighters in Syria.

While insisting he has impressed Trump’s commitment to the Middle East on allies, another underlying message – that the US stands by its friends – is gaining less traction in regional halls of power, where the Kurdish example is being viewed as a precedent.

Equally confusing to some Gulf allies is how an ever-more belligerent US posture towards Tehran can be credible when Washington’s military muscle is being called home. Pompeo has emphasised that the US has other ways of bringing Tehran to its knees, primarily through sanctions that could slow its capacity to make money in Syria, Iraq and Turkey, which are partly dependent on Tehran for energy needs.

Trump’s global mantra, of demanding allies share the burden of US defence spending, is being acted out in real terms in the region, and this was another centrepiece of the Pompeo sell.

In the past two years, Saudi Arabia has spearheaded a stagnating war in Yemen, Israel has struck Iranian targets inside Syria more than 2,000 times, and Turkey is in effect being delegated with mopping up Isis along the Euphrates River valley.

In staking his claim in Cairo, Pompeo emphasised that he identified as an evangelical Christian, and as a Christian Zionist. A large part of Trump’s domestic constituency invokes an apocalyptic showdown with a pre-ordained foe, who many followers believe to be Iran, in Israel’s northern plains that will be brought on when the world’s Jews gather in Israel.

Under Trump, such beliefs have a very real application and policy implications. Pompeo’s words and the US president’s actions have told regional leaders that there would be little talk of human rights, governance, or corruption; as long as there is common cause against Iran, autocracy is back in vogue.

As Pompeo flies back to Washington from Oman on Monday night – his last stop in Kuwait was cancelled so he could attend a family funeral – the impression he leaves is mixed. On one hand, the pre-Obama US is back; Iran is the primary foe, and Washington’s regional projection is again centred on protecting Israel. On the other, things are far less certain. While Pompeo has staked a purpose and gladhanded friends, some allies fear a volatile president’s “everyone for himself” mantra means the US may no longer have their back when it counts.