"On July 26, 36 enemy cruise missiles were destroyed," said Lieutenant General Mykola Oleshchuk on the air force's official Telegram channel.
He did not specify whether Russian missiles had hit their target during the attack.
According to the air force, Ukrainian forces intercepted three Kalibr missiles during a first series of strikes in the afternoon, and 33 X-101 and X-555 missiles in the early evening.
The missiles were fired by eight Tu-95 bombers from the southeast heading towards western Ukraine, it said.
The air force mentioned another Russian strike on Wednesday evening targeting the Khmelnytsky region in western Ukraine, which has already been targeted several times by Moscow.
It said information about that strike by MiG-31s, which launched four hypersonic Kinjal missiles, was being "clarified", but that they were particularly difficult to intercept.
In the Dnipro central region of Ukraine, the governor said on Telegram that the debris of a downed Russian missile caused a fire which was brought under control without causing any casualties.
In his evening address, Ukrainian President Volodymyr Zelensky thanked the air force for having shot down "the vast majority" of the missiles.
"I am grateful to each and every one of them who protects the Ukrainian sky," he said.
"There were a few hits, and some missile fragments fell. But it is very important that the audacity of this attack was destroyed."
Russia has increased the bombing of Ukrainian cities over the last two weeks, particularly targeting the key port of Odesa on the Black Sea.
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