The arrest attempt and a police raid on a small supporter tent encampment raised concerns that Ukraine is facing its worst political crisis since the 2014 protests that drove the pro-Russia president out of the country.
Saakashvili became a regional governor in Ukraine in 2015 at Poroshenko's invitation but they later fell out, with the former Georgian leader accusing the president of corruption.
A few hours before he was detained, Mr. Saakashvili had called for weekend protests against Mr. Poroshenko in Independence Square, an area in Kiev known as Maidan that was the center of the earlier demonstrations against Mr. Yanukovych.
A large crowd of his supporters then pulled him from a police vehicle.
On Tuesday, police tried to arrest Saakashvili at his apartment building.
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Al Arabiya quoted a source in Saleh's GPC party as saying he was killed by a sniper. "He was trying to flee to Saudi", he said. One shows a group of fighters carrying the body in a sheet proclaiming "God is Great".
"I had a constructive and open discussion with President Poroshenko on Ukraine's efforts to fight corruption", Lagarde said in a statement.
He also said the decision of the "oligarchic ruler of Ukraine" to detain Mikheil Saakashvili "was reckless".
In a televised briefing on Wednesday, Saakashvili - supporters see him as a fearless crusader against corruption - said he would not present himself to law enforcement officials, as requested by the General Prosecutor's office.
The search of Saakashvili's home was conducted two days after his Movement of New Forces party organized a rally in Kyiv calling for Poroshenko's impeachment and for legislation that would allow it to take place.
Ukrainian Prosecutor-General Yuriy Lutsenko says his office has evidence that Saakashvili's representative received $500,000 to finance protests from Ukrainian businessmen with ties to Russian Federation. Saakashvili denies the allegations against him.
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