In a statement, the 15-member Council, including India, last night expressed "deep sympathy and sincere condolences to the victims of these heinous acts and to their families, and to the people of Syria."
The statement came hours after twin suicide car bombings outside two buildings of Syria`s powerful intelligence agencies left at least 44 people dead and over 150 injured.
Syria is already facing a crisis in the wake of the 9-month uprising against President Bashar Assad`s rule.
In a departure from usual practice, the UNSC statement did not offer condolences to the Syrian government.
"The members of the Security Council reaffirmed that terrorism in all its forms and manifestations constitutes one of the most serious threats to international peace and security, and that any acts of terrorism are criminal and unjustifiable, regardless of their motivation, wherever, whenever and by whomsoever committed," it said.
In a separate statement, UN Secretary General Ban Ki-moon voiced grave concern over the escalating violence in Syria, including the suicide attacks in the capital, renewing his call for an immediate end to the bloodshed.
He urged the need for a "credible, inclusive and legitimate Syrian-led process of comprehensive political change that will address the democratic aspirations of the Syrian people," said the statement issued by his spokesperson.
Ban said the Syrian government "should fully and speedily implement the peace plan put forward by the League of Arab States."
Since the beginning of the Syrian uprising over nine months ago, the UN Security Council has remained deeply divided over the actions that should be taken against Syrian President Assad`s regime, whose brutal crackdown on civilians has resulted in the death of over 5,000 people.
European and US diplomats are demanding a resolution that imposes an arms embargo and other sanctions on Syrian regime.
On the other hand, Russia and China, which have close ties with Assad`s regime, have been opposing any kind of sanctions. They say the government forces alone are not responsible for the violence and killings but that the opposition too should be held accountable.
"If the requirement is that we drop all reference to violence coming from extreme opposition, that`s not going to happen," Russia`s envoy Vitaly Churkin said here. "If they expect us to have arms embargo, that`s not going to happen."
"We know what arms embargo means these days. It means that - we saw it in Libya - that you cannot supply weapons to the government but everybody else can supply weapons to various opposition groups."
Russia submitted a revised version of its draft resolution that called on all parties to show maximum restraint. It did not make any mention of the government crackdown on civilians.
German Ambassador Peter Wittig called the latest Russian draft insufficient. "We need to put the weight of the Council behind the Arab League. That includes the demands to release political prisoners...(and) a clear signal for accountability for those who have perpetrated human rights violations."
Wittig said Friday`s bombings are "a sign of escalation, that the situation is rapidly deteriorating." "It underlines the need ... for the Council to act: We cannot let the things just happen, we need to act here and those events underline the need to act urgently," he said.
So far, the only Council action in case of Syria has been a Presidential statement that was passed in August under India`s Presidency.