How did the clashes flare up?
Ukraine military spokesman Oleksandr Motuzyanyk said separatists backed by Moscow began attacking government positions in the eastern frontline city Avdiyivka on January 29, breaking a two-year truce agreement signed in February last year.
Twenty-seven people have reportedly died in the battered city, and nearly 300 have been evacuated.
"We have had many flare-ups before and yet somehow the sides have pulled back, reverting to an uneasy, often violent static confrontational stance," said the deputy head of the OSCE ceasefire monitoring mission in Ukraine, Alexander Hug.
Why are Ukraine and Russia at odds?
After former Ukrainian president Viktor Yanukovych suspended talks with the European Union in November 2013, tens of thousands of protesters hit the streets of the capital city, Kiev.
In February 2014 the revolution ousted Yanukovych who fled Kiev. Moscow took advantage of the chaos and annexed Ukraine's Crimean peninsula. The reason behind Russia's move is unclear but there is a lot of speculation about Moscow wanting to regain former territories of the Soviet Union.
Both sides have agreed to several temporary ceasefires after the annexation but none have held.
The US and the European Union imposed sanctions on Russia for its actions in Crimea.
Ukraine and Russia blame each other over who started the violence.
Russia says it is not directly involved in the fighting and denies supporting the rebels; Moscow says they are "volunteers."
The conflict has claimed more than 10,000 lives, and has become one of Europe's bloodiest conflicts since the Balkan wars started in 1912.
Why is Avdiyivka important?
The city is a key stronghold for the Ukrainian army because it is close to the rebel-controlled city of Donetsk which has important roads and intersections used by the rebels to transport machinery and ammunition.
Avdiyivka's coking and chemical plant is the biggest of its kind in Europe. If the rebels seize it, the supplies to Ukraine's steel industry would be cut.
How has the fighting affected the people of the city?
The heavy fighting damaged infrastructure and left thousands of civilians in both government and separatist-held territory with no access to electricity or water with temperatures plunging to minus 20C at night.
The town's heating is provided by the city's coke plant that was heavily damaged by the shelling.
"My apartment has been destroyed, what do I do? Where do I go?" a resident of the city, Anatoliy Karabass, told Al Jazeera.
Like Karabass, many of the city's 20,000 or so residents were caught in the crossfire without basic supplies.
"Does the world know what is happening to us? People are dying, suffering. We are being shelled. Without heating and electricity we nearly froze to death," another resident, Luda, told the Financial Times.
There was some respite on Monday, as the State Emergency Service said water and power supplies were being restored to the town, but not to all its surrounding villages.
"Water is running again. Much more to be done. Guns need to remain silent now," the OSCE's special monitoring mission said in a post on Twitter.
The head of the Ukraine-controlled Donetsk regional administration, Pavlo Zhebrivsky, said all schools had reopened and 500 children had turned up to study.
Local officials said over 200 tonnes of food were also being transported to the city.