The visit was on invitation from Sabah, according to a readout from the Iraqi presidency.
Both countries’ national anthems were played upon Salih's arrival.
Their meeting will be "within the framework of enhancing relations and cooperation between the two countries as well as discussing the joint dossiers between Iraq and Kuwait."
The Iraqi delegation included the Minister of Foreign Affairs, Minister of Industry, the Director of the Intelligence and the Governor of Basra.
Kuwait's state-run KUNA news agency confirmed the "high-level government delegation" meeting.
Some protesters in Basra on Saturday renewed calls for self-control, similar to the semi-autonomous Kurdistan Region
Salih has made a concerted effort to prioritize Basra, as it holds the country's most oil and gas resources, but suffers from massive corruption and poor living conditions.
Iraq's new speaker of parliament also made his first visit abroad to Kuwait in September.
Relations between Kuwait and Iraq have slowly improved since the fall of Saddam Hussein who had invaded Kuwait in 1990.
Kuwait hosted a donors’ conference early this year to attract funds to rebuild Iraq after the war with ISIS.
In April, Iraq resumed making Gulf War reparation payments to Kuwait after a three-year pause because of the conflict.
