President al-Assad says international circumstances and regional challenges require the military to be cautious, alert, ready and prepared.
"The barbaric war of annihilation the Israeli aggression is waging on our people in Lebanon and Palestine is increasing in ferocity," Mr Assad said in a written address.
Mr Assad’s comments came in spite of a renewed call by the United States President, George W Bush, for Syria and Iran to end their support for Hezbollah.
Lebanon calls for ceasefire at UN
Lebanon demanded that Israel agree to an immediate ceasefire at a special UN Security Council meeting on the new Middle East crisis.
Lebanon's acting foreign minister Tarek Mitri also sought an international investigation into Israel's bombing of the town of Qana on Sunday which he said killed 62 people, including 35 children.
Israel's ambassador to the United Nations, Dan Gillerman, said it was up to Lebanon to act to end attacks on Israel by the Hezbollah militia.
Mr Gillerman told the council that Lebanon had become "a hotbed of terrorism in a cesspool of hatred".
Israel rules out ceasefire
Israeli Prime Minister Ehud Olmert has warned Israel is not ready to stop its assault against Hezbollah.
“The fighting continues. There is no ceasefire and there will not be any ceasefire in the coming days,” Mr Olmert said.
Israel and Hezbollah continue to trade fire, less than 24 hours after Israel declared a partial halt to air strikes on southern Lebanon.
Israel had agreed to the temporary pause to allow time for an investigation into the Qana attack.
However, Israeli warplanes struck several targets, killing a Lebanese soldier near the city of Tyre.
There have also been reports of fighting on the ground in the villages of Taibe, Kila and Adasya in southern Lebanon.
The Israeli military said Hezbollah fired two shells which struck the border town of Kiryat Shmona and hit an Israeli tank near Taibe. Three soldiers were said to have been wounded in the attack.
Plea from France and Germany
French President Jacques Chirac and German Chancellor Angela Merkel have vowed to pursue efforts to find a political settlement to the crisis.
"They agreed to continue their efforts to find the terms of a political settlement as soon as possible," Mr Chirac’s office said.
Mr Chirac and Ms Merkel spoke by telephone on Monday about the crisis in Lebanon and United Nations discussions on the issue.
On Sunday France proposed a draft UN resolution that calls for an immediate cessation of hostilities in Lebanon. It was due to be examined at the UN on Monday.
France wants there to be a ceasefire and a political agreement before any multinational peacekeeping force is deployed.
Peacekeeping force extended
The UN Security Council has postponed a meeting on an international peacekeeping force for the region, instead extending the mandate of the UN Interim Force in Lebanon (Unifil) for a month.
Mr Bush said the United States would "probably not" contribute troops to a multinational force for Lebanon.
"Probably not, but we would be glad to help, you know, with logistics and/or command and control," he said when pressed on the issue during an interview with the Fox News channel.
"Most nations understand that we won't have troops there on the ground," he said.
President Bush says he is working urgently on a plan to end the violence in southern Lebanon.
“We're going to work with our allies to bring before the United Nations Security Council a resolution that will end the violence and lay the groundwork for lasting peace in the Middle East,” Mr Bush said.
UN Commissioner slams Qana attack
Meanwhile, the United Nations High Commissioner for Human Rights Louise Arbour sharply criticised Israel's bombing of Qana.
"I strongly condemn the killing of dozens of civilians, among whom a very high proportion were children, resulting from the shelling by the Israeli forces of a residential building in which civilians were sheltering in Qana, South Lebanon, on 30 July," Ms Arbour said in a statement issued in Geneva.
"I call again on all parties to the conflict to respect their obligations under international law, and to take all measures to effectively protect civilians and civilian objects," she said.
"All parties to the conflict must respect the principles of distinction and proportionality, particularly when civilians remain in the zone of military operations after a warning has been issued," the high commissioner said.
She also recalled that international humanitarian law requires all parties to avoid locating military objectives within or near densely populated areas, and reiterated UN chief Kofi Annan's call for an immediate cessation of all hostilities.