At the next meeting of the general staff, the defence minister, chief of general staff and army commander-in-chief should report to him in detail, Zelenskiy demanded in a video message on Tuesday.
"I promise the people to clarify the matter and further request the general staff not to take such decisions without me."
He said there was "incomprehension" and "outrage" in society.
Earlier, Army Commander-in-Chief Valeriy Zaluzhnyi and the general staff had said that conscripted Ukrainians needed permission to leave the place where they were registered as resident.
After criticism on social networks, it was added that this was only necessary for leaving the government district.
The basis for this is a legal norm from 1992.
Ukrainian men between the ages of 18 and 60 are subject to military service and have not been allowed to leave the country since the imposition of martial law.
From October, women in certain occupational groups will also be subject to military service.
It comes as Russian forces struck targets across Ukraine's eastern Donetsk region on Tuesday, a day after President Vladimir Putin declared victory in the neighbouring province of Luhansk after months of gruelling attritional warfare in which both sides lost many men.
Donetsk and Luhansk together comprise the Donbas, the industrialised eastern part of Ukraine.
Russia says it wants to wrest control of the entire Donbas from Ukraine on behalf of Russian-backed separatists in two self-proclaimed people's republics.
After Russian forces on Sunday took control of Lysychansk, the last bastion of Ukrainian resistance in Luhansk, Ukrainian officials said they now expect Russia to focus its efforts especially on the cities of Sloviansk and Kramatorsk in Donetsk.
On Tuesday, Russian forces struck a market and a residential area in Sloviansk, killing at least two people and injuring seven, local officials said.
A Reuters reporter on the scene saw yellow smoke billowing from a car supplies shop and flames engulfing rows of market stalls as firefighters tried to extinguish the blaze.
"Russians again deliberately target areas where civilians congregate," Donetsk regional governor Pavlo Kyrylenko wrote in a Facebook post.
"This is sheer terrorism."
Earlier, Kyrylenko had said both Sloviansk and nearby Kramatorsk had suffered heavy shelling overnight.
"They are now also the main line of assault for the enemy," he said.
"There is no safe place without shelling in the Donetsk region."
The Russian defence ministry, which says it does not target residential areas, said it had used high-precision weapons to destroy command centres and artillery in Donetsk, where Ukraine still controls a number of major cities.
UK Prime Minister Boris Johnson told Zelenskiy during a phone call on Tuesday that he believed Ukraine's military could retake territory recently captured by Russian forces.
Johnson updated Zelenskiy on the latest deliveries of British military equipment, including 10 self-propelled artillery systems and loitering munitions, which would be arriving in the coming days and weeks, a spokesperson said.
Zelenskiy adviser Oleksiy Arestovych said Russia's capture of Lysychansk and Sievierodonetsk - two medium-sized cities in Luhansk, now largely reduced to ruins - had come at a heavy human and financial cost for Russia and had taken 90 days.
"This is the last victory for Russia on Ukrainian territory," Arestovych said in a video posted online.
with Reuters
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