BAGHDAD (AP) — U.S. Secretary of State Rex Tillerson made an unannounced trip to Iraq on Monday just hours after returning from a similar surprise visit to Afghanistan, meeting the top political leaders in each of the embattled countries.

Cloaked in secrecy, Tillerson flew into Iraq from Qatar. Earlier in the day, he traveled back and forth from the gas-rich Persian Gulf country to Kabul.

In Baghdad, Tillerson was meeting with Prime Minister Haider al-Abadi for the second time in as many days to discuss reconstruction projects after the defeat of the Islamic State group in major Iraqi cities and towns. The pair will also discuss a resurgent Kurdish independence movement in the country's north, where widely-criticized independence referendum last month has sparked tensions within Iraq and with its neighbors.

Tillerson on Sunday said although the United States joined many in opposing the referendum — fearing it would distract from ongoing efforts to oust IS from its remaining strongholds — the Kurds have legitimate grievances that should be addressed within the framework of a unified Iraq.

"We did not support the Kurdish independence referendum," he said at a news conference with Qatar's foreign minister in Doha. "We did not believe it was time given that the battle to defeat ISIS is still underway. And while there have been significant victories and significant progress in Iraq, that task is not yet complete."

Still, Tillerson said he believed Abadi was committed to resolving Kurdish complaints. He called for restraint on all sides.

"We have encouraged the parties strongly to engage in Baghdad to fully implement the Iraqi constitution," he said. "The Kurdish people have a number of unfulfilled expectations, rights that were promised them under the constitution that were never delivered upon, and so there are a number of actions that need to be taken by the parties to fulfill the Iraqi constitution itself."

"We hope the Kurds will engage with Baghdad in a very productive way to see that the constitution is fully implemented," Tillerson said. "I think many of the Kurds' concerns will be addressed through that process. So we encourage the parties to not escalate the situation, not lead to conflict, and stay coordinated, and not forget that the war to defeat (IS) is not yet over and that remains the greatest threat to Iraq."

Tillerson spent the weekend making the Trump administration's case for an Arab alliance to blunt Iran's increased influence in the Middle East. He attended the inaugural meeting of the Saudi Arabia-Iraq Coordination Council on Sunday to urge the longtime rivals to set aside past differences. The administration sees an alignment of Riyadh and Baghdad as key to containing what U.S. officials refer to as "Iran's malign behavior" in the region.

Lee reported from Doha, Qatar.