Turkey faces competition from France and Italy, both of which have hosted European Championships and two World Cups each. UEFA is due to announce its decision in Geneva on May 28.
"Turkey is applying to host the championship for the third time and this is the best sign of our determination ... we are ready to give our all to provide an environment where Europe's best teams will play the best football," Erdogan told UEFA officials at a reception in Istanbul.
Istanbul's Olympic Stadium would be renovated and Galatasaray's new stadium, currently under construction, would also be used.
"I, as Prime Minister of Turkey, have presented you with a letter of guarantee worth 920 million euros," Erdogan told UEFA, adding other ministers had given additional guarantees.
"Many people think that was the best Champions League final ever, which gives me the confidence to promise you the best European championship ever held," he said.
Erdogan stressed Turkey's reputation for hospitality and the country's improving transport infrastructure.
"Not only I, but the whole Turkish nation is very excited about May 28 when the results will be announced."
