Relations between Ankara and Damascus have been frosty for decades, chilled by a border dispute, rows over shared water resources and Syria's long-time tacit support for Kurdish separatists fighting in southeastern Turkey.
The three-day visit which began on Tuesday aims to fan the spark of cooperation kindled last November when Syria handed over 22 people suspected of involvement in a wave of deadly bombings in Istanbul.
"Syria wants at least to smooth over and be sure of its Turkish front," columnist Fikret Ertan wrote in Turkey's Zaman daily, pointing to US pressure on Damascus after the Iraq war.
Turkish newspapers said the timing of a deal approved by the Israeli cabinet on Sunday to import Turkish water was far from coincidental in the light of al-Asad's trip.
Turkey, a mainly Muslim but staunchly secular state, has strong security ties with Israel.
Turkey's Foreign Ministry said talks would focus on regional and international matters as well as bilateral relations. The thaw began in 1998 when Damascus expelled Kurdish separatist leader Abd Allah Ocalan, whose PKK guerrillas had for years used Syria as a base and bolt-hole.
Then, Damascus acted only after Turkey threatened war. Now, analysts say, the spirit of rapprochement is more genuine.
The Kurdish entity
The two countries share fears that Iraqi Kurds who have governed themselves with US backing since 1991 could try to firm their autonomy into statehood, stirring separatist demands by Kurds in Turkey and Syria.
The autonomy of Iraqi Kurds is a
shared fear between two countries
In an interview with CNN Turk television on Monday, al-Asad said the creation of any Kurdish or other ethnic entity in Iraq would cross a "red line" for all Iraq's neighbours, including Syria and Turkey.
Al-Asad was answering a question about Syria's stance towards the creation of any form of Kurdish entity in Iraq - an issue US authorities say is up to Iraqis alone.
"Any division of Iraq will not affect Iraq or Turkey alone as some do believe. This would have an impact on all (of Iraq's) neighbours," said al-Asad.
Syria has traditionally sought to blend its minorities, both ethnic and religious, under a national unity umbrella. The official position of Syrian Kurdish groupings is not to pursue sectarian goals, but to safeguard their cultural identity.
"If Iraq is not united, the occupation will not end and without Iraq's unity, there will not be stability for Iraq or our countries," Al-Asad said.