Imamoglu was one of 105 people held on charges including corruption and aiding terrorist groups - a move that sparked protests.
Some protesters clashed with police in Ankara, Izmir and Istanbul, including at universities, and many rallied at a municipal headquarters in Istanbul after authorities erected barricades blocking several streets across Turkey.
Imamoglu, 54, Erdogan's main political rival, was taken in on Wednesday facing charges of graft and aiding a terrorist group, a move that the opposition condemned as a "coup attempt".
The move against the popular two-term mayor caps a months-long legal crackdown on opposition figures, which has been criticised as a politicised attempt to hurt their electoral prospects and silence dissent.
Erdogan, in his first comments on the detention, dismissed opposition criticism as "theatrics" and "slogans" for which the country had no time.
But in an interview, Ozgur Ozel, chairman of the main opposition Republican People's Party (CHP) that includes Imamoglu, said Erdogan feared facing the mayor in a vote and wanted to "take him out of the game" and cut his party's ties with the city.
He said any move barring Imamoglu from running for president in the next election would only strengthen the opposition's support, adding that the CHP will appoint him its candidate on Sunday at a scheduled vote.
From inside the police station where he was held, Imamoglu had earlier called on members of the judiciary and Erdogan's ruling party to fight the injustice of his detention.
"We must stand against this evil as a nation," Imamoglu said on social media platform X.
"These events have gone beyond our parties, political ideals. The process is now concerning our people, namely your families. It is time to raise our voices," he said.
The government denies the accusations and has warned against tying Erdogan or politics to Imamoglu's arrest, after which it imposed a four-day ban on gatherings and restricted access to some social media to restrict communications.
Civil disobedience has been dramatically curbed in Turkey since the nationwide Gezi Park protests against Erdogan's government in 2013, which prompted a violent state crackdown.
But protesters have chanted anti-government slogans in the last two days and, in Istanbul, hung banners of Imamoglu and the nation's founding leader Mustafa Kemal Ataturk alongside Turkish flags.
"They hastily detained our mayor, whom we elected with our votes," said Ali Izar, an opposition supporter on his way to work in central Istanbul.
"I do not think this is a democratic practice and I condemn it."
Amid worries about eroding rule of law and concerns over slower rate cuts, bank shares in particular tumbled on the Istanbul bourse, and the central bank hiked its overnight rate.
Authorities on Thursday seized a construction company co-owned by Imamoglu and handed control over to a court, according to the Istanbul Chief Public Prosecutor's office and financial crime investigation reports.
