The Syrian president's comments were the first he has made since Israeli war planes hit targets near Damascus over the weekend.
Mr Assad stopped short of promising retaliation, but said that the Syrians are "capable of facing Israel's ventures".
He spoke after a notorious Palestinian militant group said it had been given the "green light" by Damascus to attack Israeli targets.
The announcement by the Popular Front for the Liberation of Palestine-General Command, a group accused of an airline bombing and numerous other terrorist atrocities, came as the US Secretary of State, John Kerry, began talks in Russia in a bid to find "common ground" on Syria.
The Popular Front, which has its power base among the Palestinian refugee camps of Syria, has been authorised by President Bashar al-Assad to set up missile batteries to attack Israel, according to its spokesman in Damascus, Anwar Raja.
"Syria has given the green light to set up missile batteries to directly attack Israeli targets," Mr Raja said.
The group, which began life as a Syrian-backed Palistinian splinter faction 1968, has a long history of attacking Israeli targets, killing 47 people during the bombing of a Tel Aviv-bound Swissair plane in 1970. In 1987, a PFLP-GC guerrilla flew from Lebanon into Israel on a hang-glider and killed six soldiers before being shot dead.
Unlike some other Palestinian factions based in Syria, who have turned against the government in protest over its suppression of Syria's democratic uprising, it has remained strictly loyal to Mr Assad.
In practice, it is a relatively minor player today compared to other Islamic militant factions such as Hamas and Hizbollah. However, the prospect of Palestinian factions attacking Israel from bases outside its borders will evoke worrying comparisons with Israel's conflict with Lebanon in the 1980s, and would complicate any future peace deal.
News of the group's pledge came as Mr Kerry flew in to what many described as a lukewarm reception in Russia, which has been a strategic backer of Syria since the Cold War, and which has so far been a staunch backer of Mr Assad.
The Russian president, Vladimir Putin, kept Mr Kerry waiting for three hours prior to their meeting at the Kremlin, reportedly devoting the time to upbraiding his cabinet over domestic issues. The Russian leader then appeared unfocused during a public appearance alongside Mr Kerry, fiddling distractedly with a pen as his guest spoke.
While Mr Kerry did his best to strike a positive tone, speaking of the two superpowers' mutual interest in fighting the al-Qaeda "extremists" now dominating the rebel side of the Syrian conflict, Mr Putin made no mention of Syria at all. Mr Kerry was due to hold further talks with the Russian foreign minister, Sergei Lavrov last night (TUES), although few expected significant breakthroughs.
"The United States believes that we share some very significant common interests with respect to Syria - stability in the region, not having extremists creating problems throughout the region and elsewhere," Mr Kerry said.
Mr Kerry's visit to Moscow came after another day in which the conflict in Syria escalated on a number of fronts, mostly around the Golan Heights, a traditional flashpoint with neighbouring Israel.
Yesterday (TUES), a group of Syrian rebels calling itself the Yarmouk Martyrs Brigades abducted four United Nations peacekeepers patrolling the area, accusing them of shielding Syrian army soldiers who had killed civilians in the southern town of Wadi Raqat.
The rebel group insisted that the four Filipino peacekeepers were merely being detained for their own safety during ongoing military operations, but the UN Secretary-General, Ban Ki-moon, condemned the abductions and called for their immediate release. In early March, the same rebel group held 21 Filipino peacekeepers for four days before releasing them unharmed.
Meanwhile, Israel's Defence Minister, Moshe Yaalon, warned today that Israeli troops stationed around the Golan Heights would return fire if there was a continuation of shelling from the Syrian side. He said there had been three incidents of Syrian fire there in the previous 24 hours, although he believed it was largely fall-out from intense firefights raging on the Syrian side.
"The forces in the area are in place, and the moment there is fire from the Syrian side - they don't need authorisation from me or from the chief of staff or from the regional commander - when they identify the source of fire, they will destroy it," he said.
Mr Yaalon also denied that Israel intended to get involved in Syria's civil war, insisting that Israeli airstrikes near Damascus over the weekend were intended purely to hit Iranian missiles due to be delivered to the anti-Israeli Hizbollah militia, which the Syrian regime has long sponsored.
Hizbollah, which is backing Mr Assad, a fellow Shia Muslim, in his fight against the mainly Sunni Muslim rebels, described the Israeli airstrikes as part of an international plot to overthrow Mr Assad.
Iran, which has committed itself to Mr Assad's survival with both cash and weapons, also warned today that the conflict would get worse, not better, were the Syrian president to be toppled.
"The fallout from a vacuum in Syria will have adverse effects on its neighbours and the whole region," said Iran's foreign minister, Ali Akbar Salehi, on a visit to Jordan. "There will be serious repercussions from a vacuum. It will be grave and nobody can predict the results."
