RIYADH - Top US diplomat Rex Tillerson pursued efforts to curb Tehran's influence in talks with his country's Gulf allies Sunday, demanding that Iran pare down its involvement in Iraq as the fight against the Islamic State group draws to a close.

The question of Iranian influence in the region - including in Iraq and Qatar - is at the centre of Tillerson 's visit to Riyadh and Doha, which comes just weeks after President Donald Trump refused to certify the Iran nuclear deal and declared an aggressive new strategy against Tehran.

The US secretary of state appears focused on boosting Sunni-ruled Saudi Arabia's clout in Iraq, where Shiite forces backed by Tehran are fighting in the north, as part of a wider regional battle for influence that extends from Syria to Yemen.

"Certainly Iranian militias that are in Iraq, now that the fighting against (the Islamic State group) is coming to a close, those militias need to go home," Tillerson said at a press conference in Riyadh. "All foreign fighters need to go home."

The Popular Mobilisation Forces (PMF) - powerful paramilitary units dominated by Iranian-trained Shiite militias - have been part of the fight against IS and continue to battle different factions in Iraq. But Tillerson 's remarks were also aimed at Iran 's elite Revolutionary Guards (IRGC) and their foreign operations wing, the Quds Force, according to a senior US official.

"The position of the Iraqi government and the position of our government is that there should be a single Iraqi security force answerable to the Iraqi state," the official said on condition of anonymity.

"What happens to the PMFs is they go home or they integrate into the Iraqi security forces."

Tillerson sat in on the first meeting of a joint Saudi-Iraqi coordination council in Riyadh Sunday, which Iraqi Prime Minister Haider al-Abadi hailed as an "important step toward enhancing relations".

Saudi Arabia cut ties with Iraq in 1990 following Saddam Hussein's invasion of Kuwait, but Riyadh and Baghdad have rekindled diplomatic and commercial relations this year.

Tillerson 's visit, his third to the region as secretary of state, comes nearly five months after Saudi Arabia, Bahrain, the United Arab Emirates and Egypt cut ties with Qatar and imposed an embargo on Doha, accusing it of supporting terrorism and cosying up to Iran .

Qatar denies the charges and has rejected their terms for a settlement.

Tillerson , a former chief executive of energy giant ExxonMobil, declined to take sides in the Gulf crisis, after an unsuccessful attempt to resolve the dispute during a trip to the region in July.

"The United States maintains very strong relationships with all the countries involved in the Qatar dispute, including Qatar, and the United States intends to maintain those very strong, positive important relationships," Tillerson said in Riyadh.

"They're important from a security standpoint. They're important from an economic standpoint."

Trump had initially appeared to support Saudi Arabia in isolating Qatar but has since called for mediation, predicting a rapid end to the crisis.

Tillerson however indicated there had been little progress before he arrived at Riyadh's King Salman air base on Saturday. "I do not have a lot of expectations for it being resolved anytime soon," he said in an interview with financial news agency Bloomberg. "There seems to be a real unwillingness on the part of some of the parties to want to engage."

The State Department has said the conflict in Yemen, where Saudi Arabia and Iran back warring parties, will also figure in Tillerson 's talks in the Gulf . But on the Qatar crisis, Tillerson 's goal will be to try to persuade the two sides to at least open a dialogue.

Simon Henderson, a veteran of the region now at the Washington Institute of Near East Policy, said the disputing parties do not want to lose face.

"Tillerson will say: 'Come on kids, grow up and wind down your absurd demands. And let's work on a compromise on your basic differences'," he said.

Kuwait has tried to serve as a mediator, with US support, but the parties have yet to sit down face-to-face.

NO DIALOGUE YET BETWEEN RIVALS IN GULF CRISIS: TILLERSON

Rex Tillerson said talks between feuding Gulf states remained unlikely, as a Saudi-led boycott of Qatar nears its sixth month. "We cannot force talks among people who are not ready to talk," Tillerson said at a press conference in Doha.

"There is not a strong indication that parties are ready to talk yet," he added. "We cannot and will not impose a solution on anyone."

Tillerson 's comments came after he held talks Sunday in both Riyadh and Doha on a visit that has focused on curbing Iran 's influence in the region.

It comes just weeks after US President Donald Trump refused to certify the Iran nuclear deal and declared an aggressive new strategy against Tehran.

The visit appears aimed in part at boosting Sunni-ruled Saudi Arabia's clout in Iraq, where Shiite forces backed by Tehran are fighting in the north, as part of a wider regional battle for influence that extends from Syria to Yemen.

Tillerson also aimed to persuade the feuding Gulf states to open dialogue, according to US officials, months into a crisis that has seen Qatar isolated from its neighbours.

Saudi Arabia, the United Arab Emirates, Bahrain and Egypt in June announced they had cut all relations with Qatar, accusing Doha of ties to Islamist fundamentalists and Iran .

Qatar has denied the allegations and has rejected the conditions of a proposed settlement to the diplomatic and economic boycott.

While Trump had initially appeared to support Saudi Arabia in isolating Qatar, he has since called for mediation and predicted a rapid end to the crisis.

Tillerson , a former chief executive of energy giant ExxonMobil, had also launched an unsuccessful attempt to resolve the dispute during a trip to the region in July.

"The United States maintains very strong relationships with all the countries involved in the Qatar dispute, including Qatar, and the United States intends to maintain those very strong, positive important relationships," Tillerson said in Riyadh.

"They're important from a security standpoint. They're important from an economic standpoint."

President Trump had initially appeared to support Saudi Arabia in isolating Qatar but has since called for mediation, predicting a rapid end to the crisis.

The United States continues to support the efforts of Kuwait, which has tried to serve as a mediator in the worst diplomatic crisis to hit the Gulf in decades.

The State Department has said the conflict in Yemen, where Saudi Arabia and Iran back warring parties, would also figure in Tillerson 's talks in the Gulf .