A resolution welcoming the ceasefire, the third truce this year seeking to end nearly six years of war, was adopted unanimously by the 15-member Council, meeting in New York.
The deal, brokered by Russia and Turkey, which back opposing sides, reduced violence, but firefights, air strikes and shelling went on in some areas.
A twin suicide bombing killed at least two people in the Syrian coastal city of Tartous in an area under government control and in President Bashar al-Assad's coastal heartland shortly after midnight on Sunday, state media and monitors reported.
The attack killed at least two security officers and wounded several other people when two suicide bombers blew themselves up after being stopped, Syrian state media reported, in the first targeting of the area for several months.
Factions belonging to the Free Syrian Army (FSA) - a loose alliance of militias excluding more radical Islamist groups - said government forces and Iranian-backed Lebanese Hezbollah fighters had been trying to push rebels back in the Wadi Barada valley, northwest of Damascus.
"Continued violations by the regime and bombardment and attempts to attack areas under the control of the revolutionary factions will make the agreement null and void," said a statement from the rebel groups.
The rebels and political opposition said the government side was massing forces to launch a ground attack in the area. There has been no new announcement by the military since it launched operations in the area last week.
FSA factions said in a separate statement that they would abandon the truce deal if Russia, whose air power has helped President Bashar al-Assad to turn the tide of the war, did not use its influence to halt the Wadi Barada attacks by 8 p.m. (1800 GMT).
Later, two rebel officials said air raids around Wadi Barada had stopped just before 8 p.m. and that the ceasefire therefore still held, although clashes in the area were continuing.
The Syrian Observatory for Human Rights monitoring group confirmed that there had been fighting in the area, source of most of the capital's water, and said there had also been government shelling in the southern provinces of Quneitra and Deraa.
Russia's Defence Ministry said on Friday that rebels had violated the truce 12 times in 24 hours. Much of Friday's violence took place along the border between Hama and Idlib provinces in northwest Syria.
Russian President Vladimir Putin and Iranian President Hassan Rouhani agreed in a telephone call on Saturday to work together to try to end the Syria crisis and make a success of peace talks planned for the Kazakh capital Astana, the Kremlin said in a statement.
The British-based Observatory said the level of fighting had fallen on Saturday, and the truce was not currently at risk, although one rebel official said it was "in serious danger".
In their statement, the FSA factions said it appeared the government and opposition had signed two different versions of the ceasefire deal, one of which was missing "a number of key and essential points that are non-negotiable", but did not say what those were.
The ceasefire deal is the first not to involve the United States or the United Nations.
The Security Council welcomed the truce despite being urged by the FSA factions not to endorse the deal until the Syrian government and Russia had shown they would respect it.
The resolution also welcomed plans for the talks in Kazakhstan before a resumption of U.N.-brokered talks in Geneva in February.
The war has killed more than 300,000 people and made more than 11 million homeless.
Even with a successful truce between
Assad and the main armed opposition, the multi-sided conflict will continue.