Saakashvili denies the allegations and says Georgia's extradition request was made on behalf of "oligarchs" who fear his presence in Ukraine.
Prosecutor-General Yuri Lutsenko said late Sunday that charges would be pursued against organizers of Saakashvili's unauthorized entry.
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.
It has received the support of the former Ukrainian prime minister Yulia Tymoshenko, who went on Sunday at sti meeting in Rzeszow, in the south-east of Poland.
Saakashvili, helped by hundreds of supporters, pushed his way through a small cordon of Ukrainian border guards at the Medyka-Shehyni crossing on the Polish border yesterday.
Kiev could leave Saakashvili alone or arrest him and possibly extradite him to Georgia, where the 49-year-old is wanted on criminal charges, which he says are politically motivated.
Saakashvili meant to return to Ukraine despite being stripped of Ukrainian citizenship by his one-time ally, Ukrainian President Petro Poroshenko, and being threatened with arrest and extradition if he sets foot on Ukrainian soil.
Mr Saakashvili is a stateless person, the return to Ukraine a certain carries risk for Saakashvili, but he said he has "thousands of supporters".
When irresponsible politicians play with rules instead of following them, the one who ends up paying is the country itself.
"The main problem in our country is corruption..."
The populist Mr Saakashvili - who ran Georgia for almost a decade after leading its 2003 Rose Revolution, but is on the wanted list of its current authorities - insisted he had "no ambition towards any particular office in Ukraine". According to Groysman, Saakashvili committed an "attack on Ukrainian statehood".
Saakashvili is also wanted in his homeland for alleged abuse of power during a tumultuous nine years as president that saw him fight and lose a brief war with Russian Federation in 2008. Poroshenko stripped him of his Ukrainian citizenship. He also announced the establishment of an anti-corruption, anti-elitist political party, "citing past praise by U.S. President-elect Donald Trump for his reforms".
In December 2015, Georgian authorities stripped Saakashvili of Georgian citizenship as dual citizenship is not allowed in Georgia.
Saakashvili, a disgraced politician, boarded an Intercity train in Poland to travel to Ukraine's Lvov, but the train was delayed "because of a passenger without a right to enter the territory of Ukraine".