Aug 11 (Reuters) - Jordan's King Abdullah on Monday became the first Arab leader to visit Iraq since Saddam Hussein's fall in 2003, meeting Prime Minister Nuri al-Maliki in Baghdad.

Violence in Iraq is at a four-year low and countries in the region, especially Sunni Arab states like Jordan, are starting to re-engage with the Shi'ite-led government in Baghdad.

Following is a factbox on the region's relations with Iraq:

BAHRAIN - In June, Bahrain said it would set up a new embassy in Baghdad and was selecting an ambassador.

EGYPT - Egypt plans to send a team to Iraq to assess the security situation "within months" with a view to possibly returning an ambassador. Egypt's last envoy was kidnapped and killed shortly after arriving in 2005.

IRAN - Non-Arab Shi'ite Iran has strong ties with Iraq at many levels. Iran has a fully functioning embassy in Baghdad and President Mahmoud Ahmadinejad made a high-profile trip to Baghdad in March. Iran has links to key Shi'ite parties and politicians in Iraq. Many prominent Iraqi Shi'ites lived in exile in Iran during Saddam Hussein's rule.

JORDAN - Jordan's King Abdullah visited Baghdad on Monday and met Prime Minister Nuri al-Maliki to discuss improving security conditions in Iraq. Jordan recently named an ambassador to Baghdad, though it is unclear when he will take up the post. A truck bomb killed 17 people outside Jordan's embassy in Baghdad in August 2003.

KUWAIT - Many Kuwaitis remain bitter about Saddam's 1990 invasion of their country. The state news agency last month named Ali al-Mumin as the new ambassador to Iraq without saying when he would take up his post. Kuwait hosted a regional meeting on stabilising Iraq in April, a sign of improving ties.

SAUDI ARABIA - Oil powerhouse Saudi Arabia said last year it would open an embassy in Iraq but it has not yet upgraded ties or named an ambassador.

SYRIA - The governments of Iraq and Syria have a history of animosity since rival factions of the Baath Party took power in the two countries in the 1960s. Their embassies were shut and reopened only last year after Syria sent its foreign minister to Iraq. No ambassadors have been named and ties remain tense over accusations Syria does not do enough to stop militants crossing into Iraq.

TURKEY - Prime Minister Tayyip Erdogan visited Iraq in July, which could signal Ankara will upgrade its political ties. Relations have often been dominated by the presence of PKK Kurdish rebels in northern Iraq who launch attacks on Turkey.

UNITED ARAB EMIRATES - The UAE last month appointed Abdullah Ibrahim al-Shehhi, its envoy to India, as ambassador to Iraq. The UAE withdrew its top envoy in 2006 after a diplomat was kidnapped and held for nearly two weeks by militants.

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