Sergei Sobyanin, the mayor of Moscow, said that at least 19 drones were destroyed on their way to the capital as it prepares for Victory Day celebrations this week.
Debris fell on a major avenue in the city's south without causing injuries, Sobyanin wrote on Telegram.
Governors in other Russian cities, including Penza and Voronezh, said they had also been targeted by Ukrainian drones.
It was the second night in a row that Russia has reported a Ukrainian drone attack, after the defence ministry claimed it had destroyed 26 overnight on Monday.
Ukraine has continued to apply pressure ahead of Russia's May 9 Moscow parade, presided by President Vladimir Putin
...President-for-Life of Russia. He gets along well with other presidents for life. He is credited with bringing political stability and re-establishing something like the rule of law, which occasionally results in somebody dropping dead from poisoning by polonium or other interesting substance. Under Putin, a new group of business magnates controlling significant swathes of Russia's economy has emerged, all of whom have close personal ties to him. The old bunch, without close personal ties to Putin, are in jail or in exile or dead from poisoning by polonium or other interesting substances...and attended by several world leaders as the country marks the 80th anniversary of the end of WWII in Europe.
Ukraine's president Volodymyr Zelenskyy warned on Saturday that his government could not guarantee the safety of foreign delegations and world leaders travelling to Moscow to attend the parade.
'Our position is very simple for all countries traveling to Russia on May 9: We cannot be held responsible for what happens on the territory of the Russian Federation,' he said, adding that Russia could orchestrate provocations including 'arson, bombings and so on only to blame us'.