Earlier Friday, a barrage of rocket fire and shelling could be heard coming from the rebel-held east Damascus district of Jobar, an AFP correspondent said.
Outside Aleppo, Syrian forces that had been stationed along Castello road - a main artery into rebel-held areas of the city - were replaced by Russian troops, Rami Abdurrahman of the Observatory said.
"Mutual recriminations are being made", Kremlin spokesman Dmitry Peskov told reporters on a conference call on Friday.
Meanwhile, a senior Russian military official said Moscow would help ensure the cease-fire in Syria for another three days, but warned the United States to press the rebels to end violations of the truce.
Toner also said it is still the assessment of the United States and Russian Federation that it is worth continuing the cessation of hostilities, although he acknowledged that humanitarian aid has yet to begin flowing as called for under the agreement.
The deal calls for the truce to be renewed every 48 hours, and for Washington and Moscow to begin unprecedented joint targeting of jihadists like IS and former al-Qaeda affiliate Fateh al-Sham Front if it lasts a week.
"The truce, as we have warned - and we told the [US] State Department - will not hold out", the rebel official said, pointing to the continued presence of a United Nations aid convoy at the Turkish border awaiting permission to travel to Aleppo.
The aid impasse came as Russian Federation put pressure on the U.S. to release the text of the agreement, and urged the USA to allow it to form the basis of a United Nations security council resolution next week.
However, the Syrian government has not provided needed "facilitation letters", or permits, to allow for the start of the convoys, de Mistura said.
The Russian military has accused the Syrian opposition of using the truce to regroup and strengthen its forces.
Under the deal, Moscow must put pressure on Assad and Washington must work with Syrian rebels to silence their guns.
Russian Federation has blamed violations on the rebels, while the opposition accused al-Assad's forces of breaking the terms of the deal. The UN has said it can not cross front lines or checkpoints without Syrian permission.
Rebels say they only reluctantly accepted the initial deal, which they believe is skewed against them, because it could relieve the dire humanitarian situation in besieged areas they control, including in eastern Aleppo.
The Britain-based Observatory, which relies on a network of activists on the ground, said one girl was killed when missiles fired by rebels hit a village in the southern province of Quneitra.
The deal was struck to allow aid agencies to reach besieged populations, in the divided city of Aleppo and other areas, including embattled sites near Damascus.
Obama discussed the cease-fire agreement and the broader campaign against the Islamic State group with his national security team Friday.
Rebel groups fight alongside al-Qaida-linked militants against Assad's forces, as the extremists are among the most potent fighting forces in the country. The 20 trucks traveled from Turkey and are expected to deliver aid to a portion of Aleppo where 250,000 people are desperate for food and fuel.
Syrian state television said the government forces had foiled a rebel attack.