Fighting in parts of Syria on Sunday is endangering an already shaky ceasefire brokered by Russia and Turkey.
The efforts come to kickstart talks betwen the warring parties and have won the backing of all major world powers.
The nationwide truce between the regime and non-takfiri rebels aims to smooth the way for peace talks in Kazakhstan later this month, orchestrated by Damascus's allies Moscow and Tehran and rebel backer Ankara.
The UN Security Council on Saturday unanimously approved a resolution supporting the Russian and Turkish initiative aimed at ending the nearly six-year-old war that has killed more than 310,000 people and displaced millions so far.
Air raids and clashes have continued to shake parts of the country since the ceasefire started at midnight on Thursday, according to the Syrian Observatory for Human Rights monitoring group.
Four civilians, two of them children, and nine rebels have been killed since the truce took effect, said the Britain-based Observatory, which relies on a network of sources in Syria for its information.
In northern Syria, regime air strikes on Sunday targeted the rebel-held town of Atareb, the monitor said.
Regime air strikes also hit the Wadi Barada region near Damascus, where the government says rebels last week deliberately targeted water infrastructure that supplies the capital.
On Saturday night, rebels shelled Fuaa and Kafraya, two besieged Shiite-majority villages in northwestern Syria.
In the rebel bastion of Eastern Ghouta east of Damascus, which the government has waged a months-long offensive to retake, opposition fighters exchanged fire with regime forces.
The truce excludes the Islamic State group and former Al-Qaeda affiliate Fateh al-Sham Front.
Saturday's UN resolution "welcomes and supports the efforts by Russia and Turkey to end violence in Syria and jumpstart a political process", and hails the planned talks in the Kazakh capital Astana as "an important step".
The measure also calls for the "rapid, safe and unhindered" delivery of humanitarian aid in Syria.
60,000 killed in 2016
In Eastern Ghouta's Hammuriyeh area, Syrian activists marked the New Year by decorating a tree with lights and pictures of war victims, an AFP photographer said.
The Observatory says a total of 60,000 people lost their lives in violence across Syria in 2016, more than 13,000 of them civilians.
Syria's conflict began in 2011 with the brutal repression of anti-government protests and has since spiralled into a multi-front war involving various sides and international players.
Russia and Turkey say the Astana talks in late January will supplement, not replace, UN-backed peace efforts, including negotiations set to resume on February 8 in Geneva.
Moscow and Ankara have been working increasingly closely on Syria, including on a deal to allow the evacuation of civilians and rebels from the besieged northern city of Aleppo last month.
The fighting in Syria has occasionally spilled over into neighbouring Turkey, with several attacks blamed on IS or Kurdish militants.
In the latest violence, 39 people, including many foreigners, were killed Sunday when a gunman went on a rampage at an exclusive nightclub in Istanbul where revellers were celebrating the New Year.
No group has yet claimed responsibility for the attack.
Turkey has waged a four-month incursion in Syria that it says is to expel IS and Kurdish fighters from the border area.
Washington has been noticeably absent from the new process to end Syria's conflict, but has called the truce "positive".
Moscow — which has been supporting Damascus with air strikes since 2015 — has said it hopes to bring the administration of US President-elect Donald Trump on board once he takes office later this month.
On Saturday, in the coastal regime stronghold of Tartus, two suicide bombers blew themselves up at a security roadblock, killing two members of the regime forces.
