Russia has stopped attacks on armed groups included in the temporary truce, defense ministry official Sergei Rudskoi said.
Terrorist groups involved in the clashes, including ISIS and al Qaeda-linked al-Nusra Front, are not part of the truce agreement.
Multiple shells hit Syrian capital Saturday, the government-run news agency reported.
The shelling came from rebel-controlled neighborhoods in the capital, a military source told the news agency.
The source said the mortar shells came from the neighborhoods of Jubar and Duma, and called on Syrians living in those rebel-held neighborhoods to help stop the shelling.
"We call on the residents of these neighborhoods to put pressure on these terrorists and do not give them the opportunity to spoil the efforts to return stability and security to these areas," the military source told the news agency.
The London-based Syrian Observatory for Human Rights also reported the incidents of violence, but said things are quieter in general.
It said there were clashes between regime forces and rebels in Latakia, and other incidents of violence between government forces and ISIS fighters in Aleppo.
In Latakia, 12 rebel fighters were killed in clashes with government forces, according to the observatory.
ISIS, rebels clash
ISIS fighters also clashed with other rebel groups in Aleppo and Homs, the observatory said.
And ISIS used Twitter to claim responsibility for a suicide attack Saturday near the town of Salmiya, in Hama province.
The statement said the attack targeted regime forces gathering in Hama's suburbs.
Nevertheless, initial indications showed violence was significantly reduced -- a relief to Syrians living in the rubble of bombed-out cities.
U.N. special envoy Staffan De Mistura said reports indicated "suddenly both Daraa and Damascus had calmed down."
An unusual quiet has descended on major cities in Syria, said Rami Abdulrahman, director of the SOHR. He did note there were brief exceptions, including some unexplained explosions reported in the north.
But nobody expects peace to settle over the nation overnight, De Mistura said.
If there are violations, he said, "the important point that we need to see is that if those incidents will be quickly brought under control and contained."
'Our best chance'
Another Syria task force meeting will take place Saturday afternoon in Geneva to assess whether the truce is being respected, De Mistura said.
The cessation of hostilities is considered by some to be the most hopeful sign in years
that fighting in the nation, where the conflict has killed at least 250,000 people, will subside.
Earlier Friday, the U.N. Security Council voted unanimously in favor of a resolution backing the halt in fighting and asking for all parties to abide by the terms of the cessation.
A main Syrian opposition group, the High Negotiations Committee, said 97 of its factions agreed to respect the two-week truce that starts with the cessation of hostilities. But it warned the government and Russia not to target it under the pretense of attacking terrorist groups such as ISIS and al-Nusra Front.