US Secretary of State Mike Pompeo met Saudi Deputy Defence Minister Prince Khalid bin Salman on Monday to address the wave of escalation in the region after a US strike that killed Iran’s most senior general.

Prince Khalid arrived in Washington on Sunday, on a quickly planned visit after the US strike on Qassem Suleimani’s convoy on Friday in Baghdad. The Saudi official is scheduled to meet senior cabinet members in the Trump administration besides Mr Pompeo, including US Defence Secretary Mark Esper and national security adviser Robert O’Brien.

The state meeting was expected to address steps for de-escalation, two Saudi and US official sources told The National.

In a statement, the State Department said Mr Pompeo “thanked the Deputy Minister for Saudi Arabia’s continued support and for working with the United States to counter the threat posed by the Iranian regime".

“The Secretary underscored that the United States does not seek war with Iran and remains committed to de-escalation," it said.

Yasmine Farouk, a visiting fellow in the Middle East Program at the Carnegie Endowment for International Peace, said de-escalation was a major goal for Prince Khalid’s visit.

“The situation is worrying to Saudi Arabia,” Ms Farouk, who studies Gulf politics and visited the region last month, told The National.

“The visit is definitely to explore what the next steps are. Saudi Arabia, as we learnt from the press reports, was neither notified nor consulted ahead of the Qassem Suleimani operation."

Mr Pompeo called Riyadh twice before and after the strike but did not notify any foreign party according to The New York Times.

Ms Farouk said there was a change in tone from the US in terms of the possibility of targeting Iran. "This is worrying to Saudi Arabia, because they know that Riyadh could be the target in a retaliatory strike [by Iran],” she said.

Iraq is another area of concern for the Saudi government, Ms Farouk said. “Saudi has been steadily over the past year, and against Iran’s wishes, building its engagement with Baghdad politically and economically, and it has made critical progress.”

High-level visits have taken place and economic agreements have been signed between the Saudi Arabia and Iraq, which share an 814-kilometre border. “All of this is under threat by the instability and unfolding situation, and Saudi is on high alert when it comes to border security with Iraq,” Ms Farouk said.

The work of the coalition forces in Iraq, including the US, is paramount to Saudi security, she said, but that was threatened by Sunday's vote in Iraq’s parliament to begin the process of removing foreign troops.

Another issue of concern for Saudi Arabia when it comes to Iran is the situation in Yemen. The political office of the Houthi rebels issued a statement vowing that Suleimani’s “blood will pursue them [the US] more than when he was alive".

Weighing on the broader wave of escalation, Henry Rome of the Eurasia group, put the risk of a direct conflict between the US and Iran at “40 per cent”.

He said he expected Iran to “likely strike US military forces … despite President Donald Trump’s threats of 'major retaliation' against Iranian political and cultural sites".

He foresaw Mr Trump responding militarily to any Iranian attack, but said the outbreak of a limited or major conflict remained unlikely.

On Monday, Israeli Prime Minister Benjamin Netanyahu told his security cabinet that “Israel wasn't involved in the killing of Suleimani" and stressed "it is a US event and we should stay out of it”, the Israeli Channel 13 reported.