BAGHDAD (Reuters) - Jordan’s King Abdullah and the foreign ministers of France and Iran made separate visits on Monday to Iraq, an ally of Tehran, amid U.S. attempts to rally allies against the Islamic Republic as Washington starts withdrawing troops from neighboring Syria.

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King Abdullah’s visit, his first since 2008, follows a week after U.S. Secretary of State Mike Pompeo stopped off in both countries at the start of a Middle East tour meant to mobilize Arab countries against Iran and reassure them over the planned U.S. troop withdrawal from Syria.

The Jordanian king was greeted by President Barham Salih on a red carpet at Baghdad airport before heading to meet Prime Minister Adel Abdul Mahdi. Salih welcomed the visit as strengthening “joint interests and security”.

Pompeo, who was in Riyadh on Monday, promoted a planned Middle East Strategic Alliance (MESA) that would include Gulf Arab states, Jordan and Egypt. Washington is seeking to weaken Shi’ite Muslim Iran, Israel’s arch-foe in the region, with renewed sanctions and the support of Sunni Arab allies.

In Iraq, Washington has made overtures to officials with vague pledges of greater economic cooperation and has pressured Baghdad to stop importing Iranian gas.

But the planned withdrawal from Syria of 2,000 U.S. troops, announced by President Donald Trump last month, alarmed U.S. allies across the region, including Israel, which worries that the move could embolden Iran.

Pompeo’s tour came weeks after the announcement, and after a surprise trip by Trump to a U.S. military base in Iraq that included no meetings Iraqi leaders, prompting criticism from politicians.

Iraq’s government and many state institutions have been dominated by Iran-aligned figures and groups since the U.S.-led invasion of 2003 that toppled Saddam Hussein. Iran-backed Shi’ite militias which helped defeat Islamic State in 2017 are increasing their sway over territory and politics in Iraq.

Iran’s Foreign Minister Javad Zarif met Abdul Mahdi, Shi’ite Muslim political leaders and other officials on Sunday and Monday and said a visit by President Hassan Rouhani would follow in March, Iranian state news agencies reported.

The U.S. troop withdrawal has also alarmed Western allies who still see Islamic State as a threat, including France whose Foreign Minister Jean-Yves Le Drian met Abdul Mahdi on Monday.

Le Drian said the U.S. withdrawal “raised questions”, adding that IS had not been completely destroyed in Syria yet and threatened to return in Iraq.

France had agreed a 1 billion euro loan for reconstruction in Iraq after the 2014-2017 battle to defeat the Sunni jihadists.

Iraq has signaled it could become more military involved against IS in neighboring Syria. It has carried out several air strikes against IS in Syria in agreement with Damascus.