Sana, Syria's official news agency, said Assad and Moratinos discussed "recent developments in the region, as well as the friendly ties between Spain and Syria".
It said the two men also examined "the manner in which the European Union views a relaunch of the peace process".
Peace talks between Syria and Israel have been frozen since January 2000.
During the meeting, Assad said that "peace must be just, comprehensive" and encompass all Syrian, Lebanese and Palestinian grievances in negotiations with Israel.
The news agency quoted Moratinos as saying "Syria plays an essential role in the peace process and in stability" in the Middle East.
Moratinos said: "The purpose of my visit is to examine the peace process [with Syrian officials] to achieve a more stable situation in the Middle East".
He said his trip also aimed to "reinforce dialogue and the good relations between Spain and Syria", adding that he represented the government in Madrid, not the EU, during his trip.
Moratinos is a former European Union (EU) peace envoy to the region.
Moratinos said: "We will work with all other parties on the peace process. The EU has its own positions and undertakings and is trying to participate positively in this region".
Today's visit was Moratinos's second to Syria since the beginning of August, when he went to Damascus on the EU's behalf during negotiations leading up to the UN truce resolution that ended a month of fighting in Lebanon between Israel and Hezbollah.
The EU froze its relations with Syria after the February 2005 assassination of Rafiq Hariri, Lebanon's former prime minister, in Beirut, in which leading Syrian security officials were implicated.
An association agreement between Syria and the European Union, initialled at the end of 2004, has not yet been signed.