Speaking to Aljazeera during a recent visit to Doha, Qatar, Siniora said important steps had been taken on the part of both countries.
"We are on the first steps of solving the problems of the border and the demarcation," he said.
"Efforts started in the mid-1960s and stopped in 1975. Now we are re-discussing this matter," Siniora said.
Siniora said interaction between the two neighbours was taking place via the Syrian-Lebanese Supreme Council.
"Some areas have not been demarcated, and this is an important and necessary issue for both countries," he said.
Syria-Lebanese border issues include the occupied Shebaa Farms, a 25sq km area of fertile land claimed by Lebanon but commonly thought to be part of the Israeli-occupied Syrian Golan Heights. The UN says the area belongs to Syria.
Diplomatic representation should also be discussed, Siniora said, vowing to strive for the establishment of formal diplomatic relations with Syria.
The call was the first by a Lebanese prime minister. Lebanon and Syria have not exchanged ambassadors since the two countries became independent from France in 1943.
"Whatever the results of the report are, we all want to know who committed the crime and to ensure that they will face a fair trial"
Lebanese prime minister
Lebanese-Syrian relations should be kept separate from the results of the forthcoming report by the UN investigation into the assassination of former Lebanese prime minister Rafiq al-Hariri, he said.
On the outcome of the UN investigation into the February assassination of al-Hariri and his expectation from the UN investigator's report, Siniora said the Lebanese government's policy was not to interfere in the investigation and not to comment.
The Lebanese government has stepped up security in anticipation of the report.
"The matter of who planned and executed al-Hariri's assassination concerns the Lebanese people and the Arab world at large," he said.
"We have witnessed serial assassinations and assassination attempts after al-Hariri. Thus we have to be cautious about the prevailing security situation."
Al-Hariri and 20 other people were killed when his motorcade was blown up on 14 February in downtown Beirut. Afterwards, speculation in Lebanon was common that Syria was behind the bombing.
"The tensions surrounding the investigation report are simply based on what might result if those responsible for the assassination were to be convicted.
"Whatever the results of the report, we all want to know who committed the crime and to ensure that they will face a fair trial. Thousands of demonstrators have called for unmasking the culprits and meting out due punishment."
Security flawsIn September, four former Lebanese security chiefs were questioned over al-Hariri's murder, but Siniora said that even after the arrests, nervousness has persisted.
"The security threat was intended to reveal the incapacity of the Lebanese people to control their own security affairs and to undermine their national unity."
"We need to know who committed this crime," Siniora said.