Sunni Saudi Arabia had strained ties with Shiite Maliki, whom it accused of creating conditions for a jihadist-led offensive by marginalising Iraq's Sunni Arab minority.
"This is the good news I heard lately," the veteran diplomat said during a news conference in the western Saudi city of Jeddah, when asked to comment on Abadi's nomination.
Oil kingpin Saudi Arabia shares more than 800 kilometres of border with Iraq and has been alarmed by the jihadist offensive led by Sunni militants who have captured large swathes of its neighbour.
Maliki in turn accused Saudi Arabia of supporting "terrorism" in his Shiite majority country.
