Formerly president of Georgia and later governor of Ukraine's Odessa region, Saakashvili has been stateless since Ukrainian President Petro Poroshenko revoked his citizenship in July. He earlier was stripped of his Georgian passport. Saakashvili contends the revocation was illegal and that he wants to challenge it in Ukraine.
For weeks, he had declared plans to try to enter Ukraine at the Krakovets border crossing. Hundreds of his supporters gathered on the Ukrainian side of the crossing in anticipation.
It was not immediately clear if Saakashvili would be detained by immigration agents on the train.
The attempt to enter Ukraine carries sizeable risk. Georgia has sent Ukraine a request to extradite Saakashvili; he faces possible charges in his homeland of misappropriation of property and abuse of power while president.
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Saakashvili earlier told journalists in the Polish city of Rzeszow today: "I will not give up until I can cross the border."
Saakashvili was president of his native Georgia in 2004- 2013. He earned plaudits for fighting corruption, but sparked animosity for what critics regarded as authoritarian tendencies.