BS Yediyurappa met the family members of two persons who were killed in the firing.
Curfew was relaxed in Mangaluru on Saturday with the situation in the city peaceful after violent protests against the Citizenship Amendment Act leaving two dead in police firing.
The situation in Bengaluru and other parts of the state, where prohibitory orders were in place, was also peaceful with no major protests taking place.
Chief Minister BS Yediyurappa, who visited Mangaluru to assess the situation on Saturday, said an inquiry will be conducted into the violence that rocked the coastal city, as he announced relaxation in the curfew clamped.
"Every one wants the curfew to be revoked. I have discussed with officials and the Home minister-today from 3 pm to 6 pm it will be relaxed, during the night curfew will continue. Tomorrow curfew will be lifted during the entire day time, but it will be imposed in the night," BS Yediyurappa told reporters.
"On Monday the curfew will be revoked, but section 144 (order banning assembly of more than four people) will continue," he said, adding that people can celebrate Christmas or any other Hindu-Muslim festivities without any disturbance.
Despite prohibitory orders demonstrations had turned violent in Mangaluru on Thursday, following which police had initially clamped curfew in parts of the city until Friday night, and later extended it to the entire Mangaluru commissionerate limits till December 22 midnight.
The Chief Minister met the family members of two persons who were killed in the firing, and also held a meeting with representatives of Christian and Muslim communities, political leaders and officials.
BS Yediyurappa appealed for peace and said he has instructed the district administration to provide compensation to the families of those dead as per the provisions of law.
Noting that attempts by protesters to take the law into their hands by laying a siege to the building where firearms were stored led to "untoward incidents", BS Yediyurappa said "Home Minister and I will discuss on what kind of inquiry should be conducted... and we will get the inquiry done."
CPI Rajya Sabha MP from Kerala Binoy Viswam and some party activists who staged a protest in Mangaluru against the CAA on Saturday defying curfew, were detained, police said.
Two people were killed in police firing on Thursday as the protest against the CAA had turned violent.
Meanwhile, Mangaluru police on Saturday restricted former Chief Minister Siddaramaiah's entry into curfew clamped Mangaluru.
The Congress leader termed the action as"murder of democracy" and "undeclared emergency" as he hit out at the state government.
Citing violence in Mangaluru and curfew in place there till December 22 midnight as the reason, the Mangaluru Police Commissioner issued a notice to Siddaramaiah restricting his entry into the city till then as it may disturb peace and order.
The notice also bars Siddaramaiah from flying into the city from Bengaluru, Hubballi, Mysuru, and Goa airports and also entry through road, rail, and air. It also mentions that no one can facilitate his travel into the city.
This came a day after he had to cancel his trip to Mangaluru from Bengaluru on being informed that the chartered aircraft he was to take was denied permission to land at the airport.
Besides, a delegation of his party colleagues were detained and denied permission to meet those injured and families of the two deceased.
Alleging that his rights and freedom as Leader of the Opposition in the State Assembly have been infringed upon, Siddaramaiah declared that he will be travelling to Mangaluru on Monday and authorities can arrest him.
In Bengaluru, which witnessed large-scale protests on Thursday, police succeeded in implementing prohibitory orders by not allowing any massive protests to take place for the second consecutive day on Saturday.
Bengaluru city commissioner Bhaskar Rao claimed residents of the city and the state were largely not part of any incidents or protest.
"It is painful that those from outside the state and so called intellectuals, who are here for work and education purpose are the ones who were involved," he said.
"During the last three days cases have been registered against 244 people...yesterday also one case was registered for a derogatory poster against a community at GAS (Government Arts and Science College)..," he told reporters.
Eminent historian and writer Ramachandra Guha termed the Citizenship Amendment Act as "immoral" and "against the spirit of the Constitution" and said a wise and just government would withdraw it.
In a tweet, he also noted that immediate withdrawal of the NRC was a necessary first step to restore trust and heal the nation.
Ramachandra Guha was among many others who were detained on Thursday for staging a demonstration against the CAA and proposed National Register of Citizens (NRC) near the Town Hall at Bengaluru, in defiance of the prohibitory orders imposed in the city.