The meeting at Abdullah's palace in Riyadh was the highest-level contact in years between Shiite-majority Iraq and Sunni-dominated Saudi Arabia.
"The Iraqi president expressed his happiness to visit the kingdom and meet with his brother the king," who welcomed the visiting delegation, the official Saudi Press Agency reported.
"They discussed the latest developments on a regional and international level, as well as bilateral ties and ways to bolster them," SPA said, without giving details.
It did not say how long Masum would stay in the kingdom.
Relations were strained under Iraq's former prime minister Nuri al-Maliki, who was re-elected in 2010 after Tehran and Washington played key roles.
An American military withdrawal from Iraq the following year allowed Iran to build its political influence in Iraq.
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Saudi Arabia and Iran are regional rivals, on opposite sides in the war in Syria and other regional issues.
In June, Foreign Minister Prince Saud al-Faisal warned of the risks of civil war in Iraq with unpredictable consequences for the region and blamed Maliki's "sectarian policies" for increased violence there.
Militants, spearheaded by jihadists now known as the Islamic State group, and joined by supporters of executed dictator Saddam Hussein, took over a large chunk of northern and north-central Iraq.
Maliki's government in turn accused Saudi Arabia and Qatar of supporting "terrorism" in his country.
Relations began to improve after Masum's nomination of Prime Minister Haidar al-Abadi in August to replace Maliki.
King Abdullah sent messages of congratulation, saying he hoped Abadi's nomination would help "re-establish cohesion among Iraq's people and preserve the unity and stability of Iraq".
In September Saudi Arabia and its Gulf neighbours joined a US-led bombing campaign against the IS in Syria, although not in Iraq.
SPA said Iraq's foreign, finance and interior ministers accompanied Masum for the meetings in Riyadh, which also included Saudi Foreign Minister Faisal, Deputy Crown Prince Moqren bin Abdul Aziz, and senior security officials.