The violence came two days after a cease-fire abruptly ended.
Ukraine launched airstrikes following the end of the cease-fire on Monday.
Petro Poroshenko made a fiery speech on Monday, criticizing Russia and promising to proactively handle eastern separatists.
A Russian recession could result should the West adopt sectoral sanctions over Ukraine, but it would not be “dramatic,” Alexei Ulyukayev says.
Poroshenko signs a EU trade deal, and Ukrainians hold their breath through a weekend cease-fire extension.
Georgia and Moldova signed similar deals, while Russia immediately said "grave consequences" would follow.
Pro-Russian rebels had detained eight observers from the Organization for the Security and Cooperation in Europe.
EU leaders would discuss possible sanctions moves on Russia at their summit in Belgium starting Thursday, Kerry added.
Former President Yanukovych sparked unrest when he failed to sign the deal last fall, in favor of a fateful agreement with Russia.
Rebels shot down a Ukrainian helicopter carrying technicians who had been installing equipment to monitor violations of a peace plan in Ukraine's rebellious east on Tuesday, killing all nine people on board, a military spokesman said.
Kiev said pro-Russian rebels in east Ukraine had shot down a military helicopter, most likely killing all nine on board. It was the most serious breach of a temporary ceasefire agreed in talks between government and rebels less than 24 hours earlier.
Pro-Russian separatists reportedly killed nine military specialists in the second cease-fire violation in less than a week.
Rebel militia carried out attacks on a government military post near the rebel-controlled town of Slaviansk, a government spokesman said.
In Iraq ISIS has moved fast to seize control of large parts of the country, while violence in eastern Ukraine has raged on for months.
After failing to secure a cease-fire on Friday, Ukrainian officials and pro-Russia separatists resumed negotiations on Monday.
EU leaders will hold a summit later in the week in Brussels where they could take decisions on sanctions.
The attacks occurred in the cities of Donetsk and Luhansk.
The cease-fire extends to next Friday, but Ukraine's president said his troops will retaliate if fired upon.
Poroshenko is under pressure to secure support from Russia, as well as his backers in the West.
Ukrainian officials claimed that 300 pro-Moscow separatists were reported killed in clashes in the country's restive east.
The new fighting on Friday was about 100 km (60 miles) from the border with Russia.
