"They have done it against all the laws, what is happening here!"
Poroshenko, meanwhile, told reporters that Saakashvili was a "criminal" for entering the country against the wishes of border patrol and would be dealt with as such.
Finally, Saakashvili's supporters broke through a line of guards, the Reuters news agency reported, citing a Ukrainian border service spokesman's Facebookpost.
Earlier Sunday, Ukrainian authorities blocked a Kiev-bound train in Poland carrying Saakashvili, who eventually got off and took a bus to the Medyka crossing.
Saakashvili has said the allegations against him in Georgia are politically motivated.
Former Georgian leader Mikheil Saakashvili has vowed to stay in Ukraine to try to oust its "oligarchic" political elite, a day after forcing his way back into the country in what its president called a criminal act that must be punished.
Poroshenko's office said Saakashvili had failed to deliver change as governor, adding his Ukrainian citizenship was withdrawn because he allegedly put false information on his registration form. He had been in Ukraine since 2012, after the rise of pro-Russian politicians in Georgia who charged him with abuse of power due to his imprisonment of Georgian opposition figures on corruption charges. "I hope that this gentleman will have the same zeal to make his way to Georgia, as he tried to get to Ukraine", Poroshenko said.
Saakashvili's relationship with Poroshenko dates back almost three decades to when they were students at the same university in Kiev and their shared opposition to the Kremlin later brought them together as politicians. However, Saakashvili said in August that he is going to come back to Ukraine from Poland on September 10, 2017.
Saakashvili assures that his illegal returning to Ukraine was realized with the help of "hundreds of his supporters", and Ukrainian officials say this stateless person entered the country illegally, and 16 border guards and National guardsmen were injured.
Prosecutor-General Yuri Lutsenko said late Sunday that charges would be pursued against organizers of Saakashvili's unauthorized entry.
Mr Saakashvili, 49, is credited with pushing through pro-Western reforms in his native Georgia, which he led from 2004 to 2013 after rising to power during the so-called Rose Revolution in 2003.
Saakashvili was expected to hold a rally in Lviv on Sunday night before deciding with his supporters on whether to head to Kyiv.
"We see a roll-back of reforms in Ukraine, we see a crackdown on anti-corruption activities in Ukraine". According to the border police, 12 policemen and five border guards suffered in clashes with guards of Saakashvili.