Ukraine has a long history of corruption and shaky governance.
On Sunday, anti-corruption police said they had detained the deputy infrastructure minister on suspicion of receiving a $US400,000 ($A569,196) kickback over the import of generators last September, an allegation the minister denies.
Separately, a newspaper investigation accused the defence ministry of overpaying suppliers for soldiers' food. The supplier has said it made a technical mistake and no money had changed hands.
"There are already personnel decisions - some today, some tomorrow - regarding officials at various levels in ministries and other central government structures, as well as in the regions and in law enforcement," Zelenskiy said in his nightly video address on Monday.
His plans include toughening oversight on travelling abroad for official assignments. Several Ukrainian media outlets have reported that cabinet ministers and senior officials could be sacked imminently.
The corruption scandal could dampen Western enthusiasm for his government just as European countries bicker over sending German-made Leopard 2 tanks to Ukraine.
One of the most widely used Western tanks, Ukraine says it needs them to break through Russian lines and recapture territory this year.
Ukraine and Russia are both believed to be planning spring offensives to break the deadlock in what has become a war of attrition in eastern and southern Ukraine as the first anniversary of the Russian invasion nears.
Germany, which must approve re-exports of the Leopard, has held back, wary of moves that could cause Moscow to escalate. But under strong pressure from some of its partners, Berlin has said it is willing to act quickly if there is a consensus among allies.
Polish Prime Minister Mateusz Morawiecki, whose country borders Ukraine, said on Monday that Warsaw would seek permission to send the tanks to Kyiv and was trying to get others on board.
Germany was not blocking the re-export of Leopard tanks to Ukraine, the European Union's top diplomat said on Monday.
US State Department spokesperson Ned Price on Monday dodged repeated questions about Germany's wariness over the supply of tanks and whether the United States would support other countries supplying Leopards without Germany's approval.
"We may be hearing more from our German allies in the coming hours, in the coming days," he said at a media briefing.
The Kremlin said the splits in Europe over whether to provide tanks to Kyiv showed there was increasing "nervousness" within the NATO military alliance.
Following Ukrainian advances in the second half of 2022, front lines have been largely frozen in place for two months, despite heavy losses on both sides.
On Monday, the new general in charge of Russia's military operations in Ukraine used his first public comments to warn that modern Russia had never seen such "intensity of military hostilities", forcing it to carry out offensive operations to stabilise the situation.
"Our country and its armed forces are today acting against the entire collective West," Chief of the General Staff Valery Gerasimov told the news website Argumenty i Fakty.
Military reforms, announced mid-January, could be adjusted to respond to threats to Russia's security, which include Sweden and Finland's aspirations to join NATO and "the use of Ukraine as a tool for waging a hybrid war against our country", he said.
Russian forces were shelling and attacking Ukrainian positions on the front lines around the clock, Zelenskiy said in his address.
Ukraine says Western tanks would give its ground troops the mobility, protection and firepower to break through Russian defensive lines and resume their advance.
American lawmakers have pressed their government to export M1 Abrams battle tanks to Ukraine, saying even a symbolic number would help push European allies to do the same.
Britain has said it will supply 14 Challenger 2 tanks. French President Emmanuel Macron has not ruled out sending Leclerc tanks.
