No-one immediately claimed responsibility for the attack, which also wounded at least 30 people.
Some reports put the number of dead at 18.
Nine of those killed were reported to be soldiers who had been travelling on the bus. The army has said it believes it was directly targeted by the attack.
Mr Suleiman described the explosion as "a terrorist act".
"The army and security forces will not be terrorised by attacks and crimes that target it and civil society, and the history of the army attests to that", he said in a statement.
Syria's foreign ministry said it "staunchly denounced the criminal attack that killed many innocent civilians".
It was the deadliest incident involving the Lebanese army since fighting last year with Islamist militants at the Nahr al-Bared Palestinian refugee camp near Tripoli.
Lebanese Prime Minister Fouad Siniora has called for unity and said the government would "spare no effort" in finding and punishing those behind the attack.
Reports say at least 30 people were injured by the blast
Lebanese Information Minister Tareq Mitri told reporters in Beirut that an investigation was taking place but he did not speculate on who had been behind the attack.
"The investigation has begun and there are many interpretations, political interpretations"
"The hands of the criminals have hit in Tripoli against innocent soldiers and civilians", he said.
"Once again, they want our country to be an arena for settling scores and battling for influence."
Correspondents said it appeared the attack was intended to disrupt the groundbreaking presidential visit, which was hoped to patch up years of stormy relations between the two neighbours.
The bomb went off at a bus stop often used by soldiers in Masarif Street in Tripoli's busy commercial district.
TV footage showed the surrounding area spattered with blood and covered in broken glass. The strength of the explosion blew debris and body parts onto nearby roofs.
Witnesses said they saw men in military uniforms lying on the ground and that the dead included a popular bread vendor.
"Everybody knew him. This was his place for 30 years," said one resident.
In recent months, Tripoli has seen a series of clashes between the city's majority Sunni Muslim community, who mainly support the anti-Syrian movement, and members of the Alawite sect, an offshoot of Shia Islam, linked to the powerful political and militant group Hezbollah.
Mr Suleiman, the president, was due to travel to Syria on Wednesday for talks with his Syrian counterpart, Bashar al-Assad.
The BBC's Bethany Bell, in Damascus, says his visit marks a gradual thaw in relations between the two countries, which have been strained since the 2005 assassination of former Lebanese Prime Minister Rafik Hariri.
They planned to discuss demarcating their shared border and setting up diplomatic relations for the first time since independence in the 1940s.
Many Lebanese blame Syria for the Hariri killing, but Damascus has consistently denied any involvement.
Tuesday's vote gave the formal go-ahead for a government which brings together the anti-Syrian bloc, backed by Western powers and Sunni-led Arab governments, and former opposition groups led by Hezbollah and backed by Syria and Iran.
Mr Siniora said the bombing "will not affect the launching of our government".
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