MOSCOW—Former president of Georgia Mikheil Saakashvili said Friday that he would found a political party in Ukraine, after he accused the country’s elite of rampant corruption and quit his post as regional governor earlier this week.

In a briefing streamed online, Mr. Saakashvili called for snap parliamentary elections. He said that his party would only accept politicians and officials who had spent at most two or three years in power and would reject the influence of big business in politics.

“The...