"If they supply F-16s, and they are talking about this and are apparently training pilots, this will not change the situation on the battlefield," Putin said.
"And we will destroy the aircraft just as we destroy today tanks, armoured vehicles and other equipment, including multiple rocket launchers."
Putin said that F-16 could also carry nuclear weapons.
"Of course, if they will be used from airfields in third countries, they become for us legitimate targets, wherever they might be located," Putin said.
Putin's remarks followed comments earlier in the day by Ukrainian Foreign Minister Dmytro Kuleba that the aircraft should arrive in Ukraine in the coming months.
Ukraine, now more than two years into a full-fledged war against Russia, has sought F-16s for many months.
Belgium, Denmark, Norway and the Netherlands are among countries which have pledged to donate F-16s. A coalition of countries has promised to help train Ukrainian pilots in their use.