It was Abadi's first visit to Saudi Arabia since he became prime minister in 2014.
After a quarter century without diplomatic relations, which were cut following Saddam Hussein's 1990 invasion of Kuwait, Riyadh sent an ambassador back to Baghdad last year.
But he left amid controversy, reflecting the challenge of improving relations despite Abadi's support for better ties.
In a joint statement, Iraq and Saudi Arabia expressed "their happiness over... a qualitative leap in relations" after Abadi met King Salman on Monday.
Talks also included Crown Prince Mohammed bin Nayef and Deputy Crown Prince Mohammed bin Salman. The talks stressed the need "to explore opportunities to support economic and trade relations," the statement said. It made no mention of Gulf tensions with Qatar, but the two sides agreed to intensify efforts against extremism and "terrorism".
Abadi's visit came with the Gulf region in turmoil after Saudi Arabia, the United Arab Emirates and other allies cut ties with Qatar more than two weeks ago. They accuse Doha of supporting extremist groups, including some backed by Iran. Qatar strongly denies the charges.
Abadi, from his country's largest Shiite political bloc, is to also visit Kuwait and Iran, Saudi Arabia's Shiite-dominated regional rival.
Riyadh has long expressed concern about Iran's alleged interference in the region, including through Iraq's Hashed al-Shaabi paramilitary group which has played a major role in reclaiming parts of the country seized by the Islamic State group.
Saudi Arabia said on Monday that it captured three Iranian Revolutionary Guards aboard an explosive-laden boat heading to an oil platform in the Gulf, further ratcheting up tensions in the region. Iran said the three people detained were fishermen.