The Syrian government has called local truces near Damascus and in the northern province of Latakia but has excluded the main battlefield in Aleppo.
A new "regime of calm" began at 1am on Saturday and is scheduled to last one day in the capital's eastern Ghouta suburb and three days in the northern countryside of the coastal province of Latakia, the army said in a statement.
The truces seemed to be holding as of Saturday morning, but air strikes resumed in Aleppo, hitting at least two areas.
By excluding Aleppo, scene of the worst recent violence, the narrow truces were unlikely to resurrect a ceasefire and peace talks that have collapsed this week.
The surge in fighting in the city - home to more than two million people - showed "monstrous disregard" for civilian lives, the United Nations said.
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In the latest violence, government strikes hit three clinics in rebel-held districts of the city, rescue workers and sources in the city said.
One strike on the al-Marja neighbourhood wounded several people, including at least one nurse, the civil defence, known as the White Helmets, said.
Other medical facilities were destroyed in Bustan Qaser and al-Qoba, as well as three mosques.
No deaths were reported after the attacks but at least 10 civilians died in separate strikes in the Bustan Qaser neighbourhood.
The Syrian military denied it was behind the shelling, instead blaming "terrorists targeting citizens".
The clinic in al-Marja had been providing dental services and treatment for chronic illnesses for about five years.
Al Jazeera's Andrew Simmons, reporting from the Syria-Turkey border, said the clinic had been effectively destroyed in the strike.
"This is a medical centre that deals with chronic illnesses and dental surgery," he said. "But it is being used, obviously every facility possible is being used, for medical treatment in Aleppo right now."
|A medical facility hit by an air strike [Al Jazeera]
'Violence is soaring'
Earlier this week, at least 50 people were killed - including two doctors - when air strikes hit the Al-Quds hospital and a nearby block of flats in the rebel-held Sukkari neighbourhood, according to Doctors Without Borders.
The attack on the hospital, which is supported by Doctors Without Borders, has been roundly condemned by world leaders, including US Secretary of State John Kerry, who said it appeared to be a "deliberate strike".
More than 200 civilians have been killed in Aleppo over the past week as rebels have pounded government-held neighbourhoods with rocket and artillery fire, and the government has hit rebel areas with air raids.
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On Friday, air strikes on rebel-held districts killed two civilians, one of them a child, the Syrian Observatory for Human Rights said.
In Geneva, the UN High Commissioner for Human Rights said the latest reports of civilian deaths in Syria revealed a "monstrous disregard for civilian lives by all parties to the conflict".
In a statement released on Friday, Zeid Ra'ad Al Hussein urged all sides to step back from a return to an all-out war.
The UN official said "the violence is soaring back to the levels we saw prior to the cessation of hostilities" in late February. He added that targeting medical facilities and markets could "amount to war crimes".
Source: Al Jazeera and agencies