Nine defendants including Kavala were acquitted on Tuesday of seeking to overthrow the government with the mass "Gezi Park" protests.
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But hours later, a fresh arrest warrant was issued against the rights defender, this time linking him to the failed coup in 2016.
In a speech to his party, Erdogan again emphasised Kavala's links to US billionaire and democracy activist George Soros, suggesting this proved he was seeking to undermine the government.
"There are Soros-like people behind the curtains who seek to stir up things by provoking revolt in some countries," Erdogan said.
"The Turkey branch of this was in prison, but they dared to acquit him," he added.
He described the Gezi protests as a "despicable attack just like military coups", adding: "They were not innocent riots."
Kavala worked with Soros's Open Society Foundation before it was banned from Turkey, as well as a number of high-profile civil society groups.
The court near Istanbul there was not enough evidence to prove he orchestrated the protests as claimed by the prosecution.
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The European Court of Human Rights ruled in December that Kavala's indictment included no evidence of criminal activity and many rights groups have called his trial a mockery of justice.
The Gezi Park protests were sparked by plans to build over a rare green space in the heart of Istanbul but then snowballed into nationwide demonstrations against Erdogan's rule.
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