Syrian President Bashar al-Assad described the cessation of hostilities in force since Saturday as a "glimmer of hope" and accused the opposition of violating the agreement intended to halt nearly five years of fighting.
The opposition has in turn accused the Syrian government of breaching the fragile truce by repeatedly attacking its positions, which the government denies.
International observers have acknowledged violations of the agreement while stressing that the level of violence has decreased considerably.
"We will play our part to make the whole thing work," Assad was quoted as saying in an extract of an interview with Germany's ARD television network.
The president said the Syrian army had not reacted to truce violations in order to give the agreement a chance.
"The terrorists have breached the deal from the first day. We as the Syrian Army are refraining from responding in order to give a chance to sustain the agreement. But in the end there are limits and it all depends on the other side," Assad said.
He also said people in Syria were suffering from a "humanitarian disaster".
The war has killed at least 250,000 people and forced millions to flee their homes. The United Nations hopes the cessation of hostilities will allow it to deliver aid to more than 150,000 people in besieged areas of Syria.
The cessation of hostilities agreement, drawn up by the United States and Russia, is also seen by the United Nations as an opportunity to revive peace talks, which collapsed before they had even started a month ago in Geneva.
UN Secretary-General Ban Ki-moon and Russian Foreign Minister Sergei Lavrov said there was an urgent need to implement the agreement and for the warring parties to return to the negotiating table, a UN statement said.
"They agreed on the importance of urgently moving forward simultaneously on implementing the cessation of hostilities agreement, providing vital humanitarian assistance to civilians, and returning to political negotiations," the statement said.
US Secretary of State John Kerry said on Monday that while efforts were being made to track down alleged violations of the cessation of hostilities, there was currently no evidence to suggest they would destabilize the fragile peace.
The agreement does not include Islamic State and the Nusra Front, and Assad and his Russian backers have made clear they intend to keep attacking the jihadist groups.
The Saudi-backed "moderate" opposition says that because some of their fighters are located in areas alongside Nusra, they fear being targeted too.
The Russian Defense Ministry said it was refraining from striking areas in Syria where the "moderate opposition" was respecting the ceasefire agreement, Interfax news agency reported.
A total of 15 ceasefire violations have been registered in Syria in the past 24 hours, Interfax quoted the Russian military as saying.
The Syrian military denied it was responsible for any violations and said "terrorist groups", the term it uses to describe its enemies, were to blame. Operations against Islamic State and the Nusra Front were going ahead.
"The combat operations that the Syrian Arab Army is carrying out against Daesh [Islamic State] and Nusra are continuing according to the plans of the military command," a Syrian military source said.
Moscow, meanwhile, called for the Syrian border with Turkey to be closed. Russia's Lavrov said it was a channel being used to supply weapons to groups he described as terrorists, with some arms hidden in humanitarian aid deliveries.