Scheduled to meet al-Assad on Thursday, the trip is expected to reinforce an improvement in ties between Damascus and the Palestinian Authority.
Abbas is also due to meet the exiled heads of Palestinian factions based in Damascus amid attempts to bring them into a national unity government.
Speaking to the press about his upcoming talks, Abbas highlighted what he said was the "important and essential role of Damascus in the Middle East peace process and in Israeli-Palestinian peace".
He also pointed out that any peace "would not be complete without Israel returning all occupied Arab territory", including the Golan Heights, captured from Syria in 1967.
Syrian Foreign Minister Faruq Shara said Syria would "support the Palestinian cause and a just and durable peace" in the region.
Al-Assad and Abbas last met in December 2004, after the death of former Palestinian leader Yasser Arafat, but before Abbas was elected president of the Palestinian Authority.
Abbas is also set to meet leaders
of Palestinian resistance groups
Faruq Qaddumi, who heads the mainstream Fatah group but whose relations with Abbas are notoriously bad, met Shara in Damascus on Monday before also holding talks with the faction leaders in Syria.
The Islamist resistance movement Hamas, whose representative Khaliad Meshaal is based in Damascus, announced on Monday it would not take part in a unity government aimed at overseeing Israel's disengagement from the Gaza Strip.
Need for unity
But in his remarks, Abbas reiterated his call on all Palestinians, including Hamas, to participate in government.
"It is an important national question that interests all Palestinians and that will be pursued" following next month's Israeli withdrawal from Gaza, he said.
Relations between Damascus and Arafat varied over the decades from strained to hostile, especially after the 1993 Oslo Accords between Israel and the Palestinians, which Syria vehemently opposed.
After Damascus, Abbas is to travel to Beirut on Friday for talks with Lebanese President Emile Lahoud and leaders of the 400,000 Palestinian refugees who are based in the country, said his national security adviser, Jibril Rajub.
The trip follows a similar visit to Beirut last December by Abbas, the first by a Palestinian leader since Arafat was forced out of Lebanon a year after the 1982 Israeli invasion.