Abdullah, his half brother Crown Prince Sultan bin Abdul Aziz, and other top officials hosted Merkel and her delegation in a state banquet in the Red Sea port of Jeddah ahead of talks on regional and bilateral issues.
That followed a tour of the country's new co-educational science university, one of the key projects of Abdullah's modernisation programme.
On the second of a four-stop visit to the Gulf, Merkel flew into Saudi Arabia Tuesday from Abu Dhabi, where she called on the United Arab Emirates and Gulf countries to encourage a nuclear-free Iran and support Middle East peace efforts.
"When we look at the regional situation and the situation of the UAE, we can see how strong the interest for a peaceful solution in the Near East is, but also for an Iran that does not look for nuclear weapons," she told reporters.
"Gulf countries and in particular the UAE play an important role in the peace process in the Middle East and of course in relation with Iran," the German leader said.
Germany's secretary of state for the economy, Bernd Pfaffenbach, told AFP that Iran figured prominently in a meeting between Merkel and the Emirati president, Sheikh Khalifa bin Zayed al-Nahayan.
Talks in oil giant Saudi Arabia were expected to focus on similar issues.
Merkel first headed to the King Abdullah University for Science and Technology 80 kilometres (50 miles) north of Jeddah.
Behind high walls and tight security, the world-class post-graduate research facility allows several hundred male and female students and professors from around the world to mix freely, unlike the rest of the country where ultra-strict Islamic rules force separation of the sexes.
She toured the university's nanotechnology fabrication facility and other laboratories, some of which are equipped with state-of-the-art German machinery and instrumentation.
On Wednesday Merkel and an entourage of German businessmen are to hold meetings at the Jeddah chamber of commerce, before heading off to Qatar and Bahrain.