At least 34 migrants died when the boat they were in sank off the country's coast, the health ministry and the official SANA news agency said on Thursday.
"The number of people found dead has risen to 34," the ministry said in a statement, adding that 20 survivors were being treated in hospital.
Authorities initially reported 15 dead, before revising that figure to 28 and, shortly afterwards, revising up by a further six.
The SANA news agency reported that the migrant boat sank.
"According to survivors, their boat left Lebanon days ago," the head of Syrian ports Samer Kbrasli said in the initial statement released by the ministry of transport.
Efforts, supported by local fishermen, were ongoing to retrieve the boat, he said, but did not provide further details on what caused the incident.
Tartus is the southernmost of Syria's main ports and lies little more than 50 kilometres (30 miles) north of the northern Lebanese port city of Tripoli.
The statement published by the Syrian transport ministry said information gathered from survivors suggested the boat set off from Miniyeh, a town just north of Tripoli.
Lebanon last year saw a spike in the number of would-be migrants using its shores to attempt the perilous crossing in overcrowded boats to reach Europe.
Most of the boats head for European Union member Cyprus, an island 175 kilometres (110 miles) away.
Many of those departing from Lebanon are Syrians, but an ever-worsening economic crisis has pushed growing numbers of Lebanese to also attempt the crossing.