Saakashvili resigned as mayor of Odessa after declaring he could not remain in the position due to corruption that President Poroshenko was sponsoring and enabling.
Interior ministry adviser Anton Gerashchenko said the matter was now with the courts who had to decide whether to place the former president of Georgia in pre-trial detention.
Perceived backsliding on reform commitments, including delays in establishing an independent court to handle corruption cases, has held up billions of dollars in loans under Ukraine's $17.5 billion International Monetary Fund program.
Photo Mr. Saakashvili being detained on Tuesday.
He was speaking a day after activists and reformist lawmakers managed to derail parliamentary consideration of a bill - authored by lawmakers from Poroshenko's party and that of former Prime Minister Arseniy Yatsenyuk - that would see the head of Ukraine's National Anticorruption Bureau (NABU) removed.More news: Missing teen found with soccer coach has 'emotional reunion' with family
Lagarde said she and Poroshenko had discussed the need to safeguard the independence of NABU and similar institutions and that they agreed on the urgency of establishing an anti-corruption court.
Lithuanian President Dalia Grybauskaite said this during a joint meeting with Ukrainian President Petro Poroshenko in Vilnius on Friday, an Ukrinform correspondent reports.
"The situation with Saakashvili is not worthy of worldwide attention, because there are specific crimes that were committed and we must ensure transparency of the investigation and absolute openness", Poroshenko said.
From his jail cell in Ukraine's capital, opposition leader Mikheil Saakashvili is calling on supporters to rally for the impeachment of the president and has declared a hunger strike. Saakashvili denies the allegations against him.