The Kremlin said on Wednesday that two drones were used in the attack on Putin's residence in the walled Kremlin citadel but had been disabled by electronic defenses, Reuters reports.
It also claimed that Russia reserved the right to retaliate, a comment that suggested that Moscow might use the alleged incident to justify a further escalation in its war with Ukraine.
"Two unmanned aerial vehicles were aimed at the Kremlin. As a result of timely actions taken by the military and special services with the use of radar warfare systems, the devices were put out of action," the Kremlin said in a statement.
"We regard these actions as a planned terrorist act and an attempt on the president's life, carried out on the eve of Victory Day, the May 9 Parade, at which the presence of foreign guests is also planned ...
"The Russian side reserves the right to take retaliatory measures where and when it sees fit."
Victory Day is a major public holiday commemorating the defeat of Nazi Germany in World War Two, and a chance for Putin to rally Russians behind what he calls his "special military operation" in Ukraine.
Russia marks the occasion with a military parade on Red Square. The state news agency TASS said the parade, for which the Kremlin last week announced tighter security, would still go ahead.