The state-run news agency SANA blamed the attack on terrorists, the term the regime uses for rebels who are fighting to topple the government. There were no immediate details on the ages of the students or their identities.
But the bloodshed comes as Syrian forces fired artillery at rebel targets in and around the capital and the international community grew increasingly alarmed about the regime's chemical weapons stocks.
Syrian rebels have made gains in recent weeks, overrunning military bases and bringing the fight to Damascus. Since Thursday, the capital has seen some of the heaviest fighting since July, killing scores of people, forcing international flights to turn back or cancel flights and prompting the United Nations to withdraw most of its international staff.
"The push to take Damascus is a real one, and intense pressure to take control of the city is part of a major strategic shift by the rebel commanders' strategy," said Mustafa Alani, a Middle East analyst from the Geneva-based Gulf Research Center. "They have realized that without bringing the fight to Damascus, the regime will not collapse."
U.S. intelligence has detected signs the regime was moving chemical weapons components around within several sites in recent days, according to a senior U.S. defense official and two U.S. officials. The activities involved movement within the sites, rather than the transfer of components in or out of various sites, two of the officials said.
But this type of activity had not been detected before and one of the U.S. officials said it bears further scrutiny.
NATO Secretary-General Anders Fogh Rasmussen warned Tuesday that "if anybody uses chemical weapons, I would expect an immediate reaction from the international community."
His comments echoed a warning on Monday from President Barack Obama that there would be consequences if Assad made the "tragic mistake" of deploying chemical weapons.
Syria is believed to have hundreds, if not thousands, of tons of chemical agents, including mustard gas, a blistering agent, and the more lethal nerve agents sarin and VX, experts say.
Syria is party to the 1925 Geneva Protocol banning chemical weapons in war.
In July, Syria threatened to unleash its chemical and biological weapons in case of a foreign attack. The statement was Syria's first-ever acknowledgement that the country possesses weapons of mass destruction.
But the regime quickly tried to clarify its comments, saying "all of these types of weapons — IF ANY — are in storage and under security." That appeared to be an attempt to return to the regimes position of neither confirming nor denying whether it possessed non-conventional weapons.
NATO foreign ministers are expected Tuesday to approve member Turkey's request for Patriot anti-missile systems to bolster its defense against strikes from neighboring Syria.
Ankara, which has firmly backed the Syrian opposition, wants the Patriots to defend against possible retaliatory attacks by Syrian missiles carrying chemical warheads.
Syria is reported to have an array of artillery rockets, as well as short- and medium-range missiles in its arsenal — some capable of carrying chemical warheads.
Fyodor Lukyanov, editor of Russia in Global Affairs foreign policy magazine, said Assad will never leave without a fight because he has so few options.
"Assad realizes that there is no way back for him," said Lukyanov, a leading Russian foreign policy expert with high-level Foreign Ministry connections. "If he tries to jump the boat, his own supporters will not forgive him for doing that. And if he loses, no one will give him any guarantees."
In the Damascus area, the Britain-based opposition activist group Syrian Observatory for Human Rights said Tuesday's clashes between rebels and troops loyal to Assad were taking place in Beit Saham, Akraba and Yalda suburbs as well as near the international airport.
The Observatory relies on reports from activists on the ground.
The Damascus suburbs, which have been opposition strongholds since the uprising against Assad began in March 2011, have been the scene of heavy fighting since last week following the start of an army offensive to regain lost territory around the capital. Assad's forces have so far repelled major rebel advances on the capital, though their hold may be slipping.
SANA reported that a journalist for the state-run Tishrin newspaper was killed near his home in al-Tadhamon suburb of Damascus. Naji Assaad was "assassinated by an armed terrorist group" Tuesday morning on his way to work, SANA said. The regime refers to rebels fighting to topple Assad as terrorists.
The Syrian uprising began with peaceful protests in March 2011, but has since morphed into a civil war that activists say has killed more than 40,000 people.
Reports emerged Tuesday of at least three killings of at least a dozen people each a day earlier.
A regime shell attack on the Aleppo neighborhood of Bustan al-Qasr killed 12 men, the Observatory said. Amateur videos posted online showed bloody and dismembered bodies lying on a sidewalk in front of destroyed shops as people struggled to lift the wounded into vans and pick-up trucks.
Nearby, dozens of men stood in what the unnamed cameraman said was a bread line.
"We still see people standing in a long line despite a massacre to get bread," the cameraman says.
The Observatory also reported 13 dead in a separate attack in Aleppo's Halak neighborhood.
The group said at least 17 unidentified bodies were found in the Damascus suburb of Thiyabiyeh.
In an online video showing the dead lined up on a floor, many of their heads bloody, an off camera voice says they were shot after being detained at a government checkpoints.
The videos appeared genuine and corresponded to other reports on the incidents.
Washington has so far declined to intervene in the crisis, saying doing so could worsen the conflict.
On Monday, U.S. officials said the White House and its allies were weighing military options to secure Syria's chemical and biological weapons.
Syria is believed to have several hundred ballistic surface-to-surface missiles capable of carrying chemical warheads, and a U.S. defense official said American and allied intelligence officials have detected activity around more than one of Syria's chemical weapons sites in the last week.
As the battles rage on the ground, there was growing speculation about the fate of a top Syrian spokesman who has become a prominent face of the regime.
Lebanese security officials say Jihad Makdissi, the Foreign Ministry's spokesman, flew Monday from Beirut to London. But it was not clear whether Makdissi had defected, quit his post, or been forced out. Syria had no official comment on Makdissi, who speaks fluent English and has defended the regime's crackdown on dissent.