His visit comes with the Gulf region in turmoil after Saudi Arabia, the United Arab Emirates and other allies cut ties with Qatar two weeks ago.
They accuse Doha of supporting extremist groups, including some backed by Iran, "that aim to destabilise the region".
Kuwait, which did not follow its neighbours in severing diplomatic relations with Qatar, has been trying to mediate.
Abadi is to hold talks with Saudi King Salman, Kuwait's Emir Sheikh Sabah al-Ahmad Al-Sabah and Iranian president Hassan Rouhani during his tour of the region.
Crown Prince Mohammed bin Nayef greeted Abadi when he landed in the Red Sea city of Jeddah for the one-day visit, state media reported.
Abadi, from his country's largest Shiite political bloc, arrives at a time of heightened tensions between Sunni-ruled Saudi Arabia and its Shiite-dominated rival Iran.
Saudi Arabia cut ties with Iran early last year after years of strained relations.
Riyadh has long expressed concern about Iran's "interference" in the region, including through Iraq's paramilitary Hashed al-Shaabi which has played a major role in reclaiming parts of Iraq seized by the Islamic State group.
Gulf states are also reported to have been angered by a ransom allegedly paid by Doha to Tehran-linked militias earlier this year to secure the release of a hunting party, including members of the Qatari royal family, kidnapped in southern Iraq.
Abadi has supported efforts to improve strained Baghdad-Riyadh ties but the road to normalisation has been rocky.
Saudi Foreign Minister Adel al-Jubeir travelled to Baghdad in February for talks with Abadi, on the first visit of its kind since 2003.
In 2016, Thamer al-Sabhan became the first Saudi ambassador to Iraq in a quarter century, after ties were cut following ex-president Saddam Hussein's 1990 invasion of Kuwait.
But he left amid controversy the same year.
Although Saudi Arabia supports the fight against IS Sunni jihadists some countries, including Iraq, have argued it needs to do more to help defeat the extremists and their ideology.