A higher number of ceasefire violations were reported between Sunday and Monday evenings, compared with the previous 24 hours, the Organization for Security and Co-operation in Europe Special Monitoring Mission to Ukraine said Monday.
The Ukrainian Foreign Ministry said eight Ukrainian soldiers were killed in the Donbass region in two days.
"Russian occupation forces carried out massive attacks across the contact line using all available weapons, including (artillery, mortars and tanks) -- all prohibited by the Minsk agreements -- and small arms," the ministry said. At least 26 troops were wounded.
The US State Department on Tuesday put out a statement
saying: "The United States is deeply concerned with the recent spike in violence in eastern Ukraine around (the cities of) Avdiivka-Yasynuvata."
The Russian Foreign Ministry also expressed concern over what it calls the deteriorating situation in the Donbass.
It said Ukrainian troops "continue to conduct offensive operations to seize positions held by self-defense forces, including in the suburbs of Donetsk. Heavy weapons, including heavy artillery and multiple launch rocket systems, are being actively used to shell residential areas.
"According to the Minsk Package of Measures of February 12, 2015, such weapons should long since have been withdrawn from the contact line."
The Russian statement said there are civilian casualties, a water plant and a chemical factory have lost power, and miners lives were in danger.
The Russian Foreign Ministry warned a humanitarian and environmental disaster could take place. The two cities about 15 kilometers apart each have about 37,000 residents, according to a Ukrainian census.
The United Kingdom warned of increased fighting as well.
Foreign Secretary Boris Johnson urged restraint from both parties, and "expressed concern about the worsening humanitarian situation."
The chief monitor of the OSCE Special Monitoring Mission to Ukraine, Ertugrul Apakan, Tuesday called for the immediate cessation of fighting in the Avdiivka-Yasynuvata-Donetsk airport area in eastern Ukraine.
The UN Security Council also condemned the use of weapons prohibited by the Minsk agreement. The Security Council and the US State Department called for each side to honor the ceasefire.
Russian troops intervened in Ukraine during a popular revolution, and have remained in the Crimea region since. Putin formally announced the annexation of Crimea on March 18, 2014.