Syria and Lebanon agreed Wednesday to establish full diplomatic ties for the first time in a step toward easing tensions between the two countries that have fueled Lebanon's turmoil. Many Lebanese had long seen Syria's reluctance to establish ties as proof it never gave up historic claims that its smaller neighbor is part of its territory and that it still aims to dominate Lebanon. The step is a significant symbolic victory for them, seen as Damascus' formal acknowledgment that Lebanon is an independent nation. But Syria only agreed to formal ties after its influence in Lebanon was guaranteed by the creation on Tuesday of a unity government in Beirut that gives Damascus' ally Hizbullah a strong say in decision-making. Still, the agreement - along with the unity government - could go a long way to easing three years of continuous crisis in Lebanon, where the power struggle between pro-Western and pro-Syrian factions brought the country to the brink of civil war. Much depends now on how well the sides, who remain rivals, get along: An attempt by either to dominate could spark new tensions. Syria controlled Lebanon for nearly 30 years since the 1970s, when it sent its army into the country as peacekeepers during its 1975-1990 civil war. Its direct hold was broken in 2005, when anger over the assassination of former Lebanese prime minister Rafik Hariri - which many blamed on Damascus - forced it to withdraw its troops. Even after the withdrawal, anti-Syrian Lebanese accuse Damascus of trying to maintain its influence, saying it was egging Hizbullah to topple the Western-backed government of Prime Minister Fuad Saniora. They also accuse Syria of being behind a string of assassinations of anti-Syrian figures since 2005 to intimidate Beirut and destabilize the country. Syria denies a role in those attacks or the Hariri killing. The decision to open embassies in one another's capitals came during a landmark visit to Syria by Lebanese President Michel Suleiman - the first such visit by a Lebanese head of state since the Syrian troop withdrawal. Suleiman and his Syrian counterpart, President Bashar Assad, decided Wednesday "take the necessary measures...to establish diplomatic relations...on the level of embassies in accordance with the United Nations charter and international laws," said Assad's adviser Buthaina Shaaban. No date was given for the embassies' openings. The United States, which backs Saniora, welcomed the decision but pushed for Syria to stay out of Lebanese affairs. "We have long stood for the normalization of relations between Syria and Lebanon on the basis of equality and respect for Lebanese sovereignty. One of the steps that has long been required is the establishment of a proper embassy for Syria in Lebanon and vice versa," Secretary of State Condoleezza Rice said. "Now, if the Syrians will go ahead and demarcate the border between Lebanon and Syria, and respect Lebanon's sovereignty in other ways, then this will have proved to be a very good step," she said. Syrian official news agency SANA reported that Suleiman and Assad also discussed the issue of formally demarcating the country's shared border, another step called for by many Lebanese lawmakers. The new progress comes after Lebanon appeared about to break into a new civil war in May, when Hizbullah fighters battled with Saniora supporters and seized parts of Beirut. But the factions reached a deal brokered by Qatar to end the fighting, agreeing to elect then-army chief Suleiman president - a post left empty for months - and to form a unity government that would give Hizbullah and its opposition allies enough seats in the Cabinet to veto major decisions. It tooks weeks of negotiations between the factions, but the unity government was approved by parliament on Tuesday. Assad had first raised the idea of establishing ties to Suleiman when they met in Paris last month on the sidelines of a Euro-Mediterranean summit. Assad told Suleiman the step was possible once a unity government was confirmed. State-run Syrian newspapers welcomed Suleiman's visit, saying it would put Syrian-Lebanese relations back on track. The Tishrin newspaper said in an editorial that the visit would "lay the foundations for a new phase of brotherly relations." "Welcome President Michel Suleiman. Welcome Lebanon," headlined al-Thawra newspaper.