The latest violence came as the leaders of France, Germany, Russia and Ukraine called for the implementation of a peace deal in the separatist east during late-night talks on Monday.
Ukraine also called for an OSCE "police mission" while the Kremlin said it backed an expanded monitoring mission in the east of Ukraine.
"As a result of shelling, seven Ukrainian soldiers have died and nine received injuries over the past 24 hours," Oleksandr Turchynov, secretary of Ukraine's National Security and Defence Council, said in a statement.
He claimed Russia was massing heavy weapons along a demarcation line in the east, adding that over the past month Ukraine had detected an increased number of Russian reconnaissance and other unmanned aerial vehicles.
Military spokesman Oleksandr Motuzyanyk said the deaths represented "extremely heavy losses" for the Ukrainian forces.
Yesterday, the leaders of France, Germany, Russia and Ukraine spoke by phone and called for the 2015 peace accords signed in Minsk to be implemented "as quickly as possible," according to the office of French President Francois Hollande.
The Kremlin said that Germany, France and Ukraine had received proposals concerning local elections in the rebel east, the regions' special status and decentralisation, noting they had been agreed with pro-Russian insurgents.
Persistent violence is preventing the warring sides from reaching a firm political reconciliation deal despite a series of truce agreements that have helped reduce the fighting over the past months.
Poroshenko's office said that the leaders of Ukraine, France, Germany and Russia expressed support for the deployment of an OSCE police mission to eastern Ukraine and the start of consultations on the subject.
"In our understanding, this is not a police mission," Kremlin spokesman Dmitry Peskov told reporters today of the OSCE monitors in east Ukraine.
But he said that "indeed this subject is being discussed," noting that the mission's arms policy was under question.
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