Alexander Lukashenko was unexpectedly sworn in to his sixth term in office on Wednesday after an election the opposition says was rigged.
Thousands of Belarusians took to the streets of the capital of Minsk and other cities afterwards.
Police fiercely dispersed the crowds, with officers in the capital using truncheons and water cannons, leaving dozens injured.
The country’s Interior Ministry said on Thursday that 364 people were detained the previous night, including 252 in Minsk.
The vast majority of them remain in custody, awaiting a court hearing.
Despite the crackdown, rallies continued on Thursday morning, with hundreds in Minsk forming human chains of solidarity in parts of the city and obstructing road traffic by driving slowly or stopping altogether, honking in protest.
Mr Lukashenko’s inauguration was not announced in advance and came as a surprise for many after nearly seven weeks of mass protests against his disputed re-election.
You know, about 2,000 people, together with the military, were invited to the inauguration
Opposition leaders dismissed the ceremony “a farce” that had been prepared in secret, while many European officials refuse to recognise Mr Lukashenko as the country’s legitimate president.
The president argued on Thursday that the inauguration was not prepared in secret and bristled at Western criticism.
“You know, about 2,000 people, together with the military, were invited to the inauguration,” he said.
“It is practically impossible to keep it secret.
“You know, we didn’t ask anyone to recognise or not recognise our election, the legitimacy of the newly elected president … the important thing is that it’s in accordance with the constitution.
Mr Lukashenko, 66, has run Belarus, an ex-Soviet nation of 9.5 million, with an iron fist for 26 years.
Official results of the country’s August 9 presidential election had given him 80% of the vote, with his strongest opponent, Sviatlana Tsikhanouskaya, getting 10% support.
But both opposition members and some poll workers say the vote was rigged.
Ms Tsikhanouskaya has not accepted the outcome of the election as valid and neither have the thousands of her supporters who have been demanding Mr Lukashenko’s resignation at daily rallies all over the country for nearly seven weeks in a row.
The country’s prosecutor general Andrei Shved on Thursday threatened protesters with “significant” fines and said authorities are seeking to adopt stricter punishments for parents “who are involving children in protest actions”.
Prosecutors in Minsk have already handed 140 warnings to families that took children to anti-government rallies.
