(Adds Rice's comment)
DAMASCUS, Aug 13 (Reuters) - Syrian President Bashar al-Assad and Lebanese President Michel Suleiman agreed on Wednesday to establish diplomatic relations between their countries at ambassadorial level, a Syrian official said.
Damascus has been under pressure from the United States and other governments including France to treat its smaller neighbour more as a sovereign state by taking steps including opening a Beirut embassy and demarcating borders with Lebanon.
"The two presidents ... have instructed their foreign ministers to take the necessary steps in this regard, starting from today," Buthaina Shaaban, an adviser to Assad said.
The United States welcomed the move.
"We have long stood for the normalization of relations between Syria and Lebanon on the basis of equality and respect for Lebanese sovereignty," U.S. Secretary of State Condoleezza Rice told a news conference in Washington.
"One of the steps that has long been required has been the establishment of a proper embassy for Syria and Lebanon and vice-versa," she added.
Syria had dominated Lebanon until the 2005 assassination of former Prime Minister Rafik al-Hariri triggered pressure for it to end a 29-year military presence in the country.
Suleiman, who had been army chief before his election, was received at a hilltop palace overlooking Damascus. He was appointed head of Lebanon's military when Syria still controlled the country and describes his ties with Damascus as excellent.
The two countries announced last month in Paris that they intended to open diplomatic relations for the first time since they gained independence in 1943. Wednesday's agreement formally set those ties on the highest level.
It was Suleiman's first visit to Syria since his election in May as part of a Qatari-mediated deal that defused a bitter political conflict between an anti-Syrian majority coalition and an alliance of groups backed by Damascus.
Syrian Foreign Minister Walid al-Moualem told Lebanon's as-Safir newspaper that Suleiman's visit was "a starting point and a true foundation for future relations".
Syria's opponents in Lebanon, including Saudi-backed politician Saad al-Hariri, have accused Damascus of assassinating Rafik al-Hariri and other anti-Syrian figures and fomenting instability since its withdrawal. Syria denies the allegations.
In a sign of lingering insecurity in Lebanon, a bomb in the northern city of Tripoli killed at least 18 on Wednesday, including nine soldiers. Syria condemned the attack.
DRESSING THE WOUNDS
Moualem said Lebanon and Syria must decide whether they wanted to "open the wound or dress it and move forward".
"We are comfortable with the sequence of positive developments in Lebanon," he said, in reference to the Doha agreement which ended 18 months of political conflict.
The deal effectively gave Syria's allies in Lebanon, led by the powerful Hezbollah guerrilla group, the power of veto over the government.
Saad al-Hariri, Rafik al-Hariri's son and political heir, told journalists on Tuesday he would not visit Damascus, but hoped Suleiman would return with "excellent results".
The summit agenda included the fate of hundreds of Lebanese who went missing during the era of Syria domination and whose relatives hold Damascus responsible for their disappearance.
Economic and water agreements that anti-Syrian Lebanese politicians regard as unequal are also expected to be discussed. (Additional reporting by Tom Perry in Beirut and Sue Pleming in Washington; editing by Sami Aboudi)
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