Moratinos made the announcement after talks in the Spanish capital with Palestinian chief Mideast peace negotiator Saeb Erekat.
Abbas was in Madrid on his way to Jordan and then an African Union summit next week in Addis Ababa, after attending the annual World Economic Forum in Davos, Switzerland.
Abbas earlier held talks with Spanish Prime Minister Jose Luis Rodriguez Zapatero at which the Spanish leader underlined Madrid's commitment to finding a settlement to the conflict in the region.
Spain two weeks ago hosted an international meeting in Madrid to mark 15 years since a full-blown Middle East conference in the city at which participants urged a new impetus to revive the stalled process.
Spain offering Palestinians increasing support
Moratinos, former EU Mideast envoy, used the occasion to continue Spanish lobbying to host another conference and proposed Arab participation in the "Quartet" comprising the United Nations, the United States, the European Union and Russia.
On Saturday, Abbas was to wind up his Spanish visit by meeting the leader of Spain's main conservative opposition Popular Party, Mariano Rajoy, and the leader of the pro-Communist United Left, Gaspaz Llamazares, the leaders' parties said.
Spain has offered the Palestinians increasing support seeing the Middle East as a key focus of its diplomatic efforts, with aid reaching 31.5 million euros (USD 40.7 million) in 2005 and 46.8 million euros (USD 60.5 million) last year, according to official figures.