Hariri's second official visit to Damascus follows accusations by Israel and the United States that Syria and Iran are continuing to supply the Lebanese Shiite movement with arms and undermining regional stability.
The Lebanese premier is due to visit the United States at the end of May for a meeting with President Barack Obama, and is expected to address the United Nations Security Council, of which Lebanon is currently a non-permanent member.
Syrian presidential adviser Bussaina Shaaban hailed the improving ties between Damascus and Beirut, in comments published on Tuesday in the pro-government newspaper Al-Watan.
"Since his last visit to Damascus, relations (between the two countries) have deepened...President Assad warmly welcomes this visit, designed to coordinate policy ahead of (Hariri's) trip to Washington," she said.
"We look favourably on every Arab visit to Washington that explains the Arab position."
Israeli President Shimon Peres sparked controversy last month when he accused Syria of supplying Hezbollah with Scud missiles, a charge Damascus has staunchly rejected.
US Defense Secretary Robert Gates made similar allegations at the end of April, saying Syria and Iran were providing Hezbollah with rockets and missiles of ever-increasing capability.
During Hariri's December visit to Syria, the first since the 2005 assassination of his father, ex-premier Rafiq Hariri, he expressed his desire for "privileged, sincere and honest relations...in the interest of both countries and both peoples."
Hariri and his US- and Western-backed allies have in the past blamed Syria for the murder and for a string of subsequent political assassinations in Lebanon. Damascus has denied any involvement.
Syria dominated its tiny neighbour for nearly three decades until April 2005 when it pulled out its troops from Lebanon under international and regional pressure, two months after the assassination of Rafiq Hariri.
The two countries established diplomatic ties for the first time in 2008, with Syria opening an embassy in Beirut, while Lebanon opened its mission in Damascus in March 2009.
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