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Abadi hailed the meeting as an "important step toward enhancing relations", echoing similar comments from King Salman.
"We are facing in our region serious challenges in the form of extremism, terrorism as well as attempts to destabilise our countries," the Saudi monarch said.
"These attempts require our full attention."
Iraq is seeking economic benefits from closer ties with Riyadh as both countries suffer from a protracted oil slump.
Saudi Arabia is also seeking to counter Iranian influence in Iraq.
"This event highlights the strength and breadth as well as the great potential of the relations between your countries," Tillerson said, referring to the meeting.
After former dictator, Saddam Hussein's August 1990 invasion of Kuwait, Riyadh severed relations with Baghdad and closed its border posts with its northern neighbour.
Ties remained strained even after Saddam's ouster in the 2003 US-led invasion of Iraq, since when successive Shiite- dominated governments in Baghdad have stayed close to Tehran.
But a flurry of visits between the two countries this year appears to indicate a thawing of ties.
Abadi's tour coincides with Saudi Energy Minister Khaled al-Faleh's high profile visit to Baghdad on Saturday where he called for the strengthening of economic relations to boost oil prices.
At the opening of the Baghdad International Fair, Falih hailed what he called "the new Iraq, on the ambitious road to prosperity and growth while strengthening its relations with the world".