In an address on Friday to the UN Security Council following a visit to Washington, Siniora said a positive response on these issues would signal that Syria "is beginning to accept the idea that good (bilateral) relations are possible."
He stressed the need "to restore confidence between the two countries" and for "a genuine acceptance by the Syrian government of a truly independent Lebanon."
Syria withdrew its troops from Lebanon in 2005 after 29 years of military and political domination of its smaller neighbour, in line with UN Security Council Resolution 1559 passed the previous year.
Siniora also made it clear that an Israeli withdrawal from the disputed Shebaa Farms, which Beirut regards as Lebanese territory, was a "priority national issue."
"It is incumbent upon Israel to withdraw from it, hand over the Lebanese detainees in its prisons, submit the maps of the landmines it left in the South, and stop its infringements on Lebanese sovereignty," he said.
"We look forward for an active role by the UN in helping us achieve those demands," he added.
Milad Atieh, Syria's UN deputy representative, responded by restating Damascus's willingness to demarcate the borders, although he said this could not be done in the Shebaa Farms area because the area "is under Israeli occupation".
Roed-Larsen (L) is tasked with
settling the border dispute
"Israel must withdraw from the occupied territories before our two countries can demarcate their borders," Atieh said.
On diplomatic relations, he said: "if there is mutual will... that matter can be considered."
Jean-Marc de la Sabliere, France's UN envoy, meanwhile welcomed Siniora's briefing in the Security Council, saying it showed "a true vision to achieve Lebanon's full independence and sovereignty."
"We expect Syria to answer and to show a genuine commitment to the independence of Lebanon, to pacified relations with its neighbour and to regional stability," he added.
On Tuesday, Terje Roed-Larsen, the UN envoy who is tasked with settling the Syrian-Lebanese dispute, urged the two to agree on demarcating the border in the Shebaa Farms area, a small mountainous territory at the convergence of the Lebanese-Syrian-Israeli borders.
Israel captured the area from Syria in the 1967 Middle East war, and it is now claimed by Lebanon with Damascus's consent.
Israeli troops have retained control of the area since their withdrawal from south Lebanon in May 2000. It remains the scene of clashes between Israeli forces and the Hezbollah militia.
The United Nations regards Shebaa Farms as Syrian territory.