Student-led protests have swept through downtown Tirana and spread to other cities this month, angered by what is perceived as government corruption, as well as a lack of job opportunities and poor educational standards,.
Protesters demanding Rama's resignation set fire to government buildings and banks, smashed shop windows, and uprooted paving stones to hurl at the police.
Rama said in a televised address, "I believe those demanding my resignation are mistaken if they think they can impose it through violence or any other means, but I do not believe that everything they say or demand is wrong."
The unrest followed peaceful protests over the summer against a luxury coastal real estate development project backed by Jared Kushner, son-in-law of U.S. President Donald Trump, posing the biggest challenge yet to Rama, who has governed since 2013 and won a fourth term last year.
Earlier in the day, Rama implemented new measures to curb violence, including a fine of 500,000 leks ($6,188) for anyone who participates in a protest that turns violent, even if they did not commit acts of violence themselves.