Can I extend my stay in the U.S. on F-1 visa if I am unable to complete my studies in the assigned time?

Yes, you may apply for extension of stay if you need extra time to complete your studies. Your Form I-20 can be extended by the designated school official. The I-20 extension should be filed along with your passport, Form I-94, Arrival-Departure document, a letter stating the reason for your extension.