Georgian prosecutors circulated tapes earlier this week allegedly showing the businessman offering a $100 million bribe to a senior Interior Ministry official to "neutralize" the department during protests planned for the January presidential elections.
Patarkatsishvili, Georgia's richest man, who lives in Britain, has admitted attempting to bribe the official, but said he had only been trying to deter clashes between police and protestors after the elections, if Mikheil Saakashvili's reelection bid was successful.
"I am ready to give up plans to run in the presidential election and send a relevant statement to the Central Election Commission," the businessman said in a statement in London.
A member of Patarkatsishvili's campaign headquarters in the Georgian capital, Tbilisi, earlier said the tycoon could pull out of the race on condition Saakashvili, who stepped down in late November to be able run, did the same.
Authorities in the ex-Soviet Caucasus state had already accused Patarkatsishvili of seeking to instigate a coup during street protests in Tbilisi in early November, which were brutally broke up by riot police and eventually led to the U.S.-educated Saakashvili announcing the snap polls.
The billionaire was reported to have delayed his arrival in Georgia over fears he would be arrested.
Patarkatsishvili's press service said on Thursday the businessman would make a televised address to Georgians from London soon.
