Zelenskiy, in a weekend video address, said Moscow could try "something particularly ugly" in the run-up to Wednesday, which also marks half a year since Russia invaded.
Local authorities in Kyiv have banned large public events, rallies and other gatherings related to the anniversary from Monday until Thursday due to the possibility of rocket attacks, according to a document published by the Kyiv military administration.
Fears of intensified attacks were likely to rise after Russia's Federal Security Service (FSB) accused Ukrainian secret services on Monday of killing Darya Dugina, daughter of a Russian ultra-nationalist ideologue, in a suspected car bombing on Saturday, Russian news agencies reported. Ukraine has denied being involved.
The capital, Kyiv, is far from front lines and has only rarely been hit by Russian missiles since Ukrainian defenders repelled a Russian ground offensive to seize the capital in March.
In Kharkiv, a northeastern city that has come under frequent and deadly longer-range artillery and rocket fire, Mayor Ihor Terekhov announced an extension to an overnight curfew to run from 4 p.m. to 7 a.m. effective from Tuesday to Thursday.
The Office of the U.N. High Commissioner for Human Rights, citing its monitoring mission in Ukraine, said on Monday 5,587 civilians had been killed and 7,890 wounded as of Aug. 21, mainly from artillery, rocket and missile attacks.
In a phone call on Sunday, U.S. President Joe Biden, German Chancellor Olaf Scholz, French President Emmanuel Macron and British Prime Minister Boris Johnson welcomed recent discussions on enabling a mission by the U.N. nuclear watchdog agency to the Russian-held Ukrainian Zaporizhzhia nuclear power plant.
Overnight, Russian forces fired rockets into Nikopol, just across the Dnipro from the plant on its south bank, as well as the Krivyi Rih and Synelnykovskyi districts further out to the northwest and northeast respectively, regional Governor Valentyn Reznichenko wrote on Telegram.
Moscow requested a U.N. Security Council meeting be held on Tuesday to discuss the plant, Russian state-owned news agency RIA reported, citing Deputy Ambassador to the U.N. Dmitry Polyanskiy.
In the latest sign of a planned Ukrainian counter-offensive to retake the Russian-occupied Kherson region in the south, smoke was rising from the sole bridge across the Dnipro in Kherson city, a Kyiv interior ministry adviser said.
A source in occupied Kherson's emergency services told Russia's Interfax news agency that the Antonivskyi bridge was hit by high-precision HIMARS rockets supplied to Ukraine by the United States, and that 15 people had been injured.
The bridge, a key crossing for Russian military transport in the region, has been repeatedly targeted by Ukrainian forces.
In eastern Donetsk province, Russian artillery and multiple rocket launchers battered Soledar, Zaytseve and Bilohorivka near the city of Bakhmut, and at least two civilians were killed, Ukrainian authorities said. Russia denies targeting civilians.
Reuters was not able to independently verify the battlefield reports of either side.