Ukrainian authorities said Russian drones, bombs and artillery shelling struck civilian areas of the northeastern Kharkiv and southern Kherson regions, killing at least two people and wounding seven others.
Russia's defence ministry on Sunday accused Kyiv of committing more than 1000 ceasefire violations, state media reported.
Similar ceasefires announced since Russia invaded its neighbour more than four years ago have also failed to stop the fighting, and US-led diplomatic efforts in the past year have come to nothing.
The Washington-based Institute for the Study of War said data from NASA observations indicated military activities decreased but did not stop after Trump announced on Friday that Russian President Vladimir Putin and Ukrainian leader Volodymyr Zelenskiy had accepted his request for a ceasefire running Saturday through Monday.
The move was meant to mark Victory Day, the Russian celebration marking the defeat of Nazi Germany.
The ISW noted late on Sunday that "ceasefires without explicit enforcement mechanisms, credible monitoring, and defined dispute resolution processes are unlikely to hold".
Trump had said there would also be an exchange of prisoners, declaring that the break in fighting could be the "beginning of the end" of the war.
Zelenskiy said the exchange of 1000 prisoners from each side was being prepared.
There are no signs that the two sides are ready to budge from their key negotiating positions, however.
Putin wants all of the Donbas region, Ukraine's industrial heartland, even though his army has not completely captured it, but Zelenskiy wil not surrender it.
Zelenskiy has offered a ceasefire and a face-to-face meeting with Putin, which the Russian leader has ruled out until a negotiated settlement is almost finalised.
Putin suggested at the weekend that former German chancellor Gerhard Schroeder, who has had close business ties to Russia, could act as a mediator.
But German and European officials scotched that possibility even while accepting that the European Union could take a more significant role in peace efforts are being largely sidelined by Washington in the past year.
Even so, EU foreign policy chief Kaja Kallas said the bloc must get its objectives straight before attempting to negotiate with the Kremlin.
"Before we discuss with Russia, we should discuss amongst ourselves what we want to talk to them about," she told reporters in Brussels.
Ukrainian Foreign Minister Andrii Sybiha joined EU foreign ministers for the Brussels meeting.
"We have mainstream peace talks under the leadership of the US, and we need this track and we need US leadership. But Europe could play also its role," Sybiha said.
He noted that in recent months Ukraine had improved its performance on the battlefield, reducing the bigger Russian army to a slow and costly slog on the 1250km front line, while using its domestically developed long-range drones and missiles to hit targets deep inside Russia.
"We have a new reality on the battlefield ... Ukraine became stronger after the most difficult winter," Sybiha said.
German Defence Minister Boris Pistorius was the latest senior European official to visit Kyiv, arriving on Monday on an unannounced visit that was set to focus on furthering defence co-operation between the two countries.
