BS Yediyurappa said there was no need to panic as coronavirus cases were "well under control".
Prime Minister Narendra Modi has asked Karnataka to focus on Bengaluru, and the districts of Kalaburagi and Bidar bordering Maharashtra given the rising coronavirus cases in these regions, Chief Minister BS Yediyurappa said on Wednesday.
Addressing reporters after the Prime Minister's video conference with chief ministers on the surge in COVID-19 cases in some states, Mr Yediyurappa urged people to people to follow the coronavirus safety rules.
"As cases are going up in Bengaluru, Kalaburagi and Bidar which are located at the border of Maharashtra, Prime Minister Narendra Modi asked us to focus on these three districts," Mr Yediyurappa told reporters.
"The state has seen the peak from August to October 2020. Cases started declining in November 2020, but the decline was faster from December 2020. During the last about 10 days, the Covid cases are showing an increasing trend. The positivity rate has also increased to 1.65 per cent as of March 15," he said.
He, however, said there was no need to panic as the cases were "well under control".
Quoting the Prime Minister, Mr Yediyurappa said there was an adequate supply of vaccines.
He added that coronavirus can only be controlled but cannot be wiped out completely.
Ruling out any curfew, the Chief Minister appealed to the people to use masks and maintain physical distancing.
He also asked people to be extremely careful during gatherings within four walls.
However, there will not be any restrictions on public gatherings during the by-elections to the Belagavi Lok Sabha constituency and Maski and Basavakalyan assembly segments.
According to the Chief Minister, Union Home Minister Amit Shah appreciated Karnataka for conducting over 93 per cent RT-PCR tests.
The Prime Minister insisted that vaccines should be utilised optimally with less wastage.
Mr Yediyurappa briefed PM Modi of the state government targets of vaccinating 3 lakh people every day and its plan to take up the drive at old-age homes and mega residential complexes.
Out of some 2,000 centres selected for carrying out the vaccination drive, more than 1,400 are yet to resume their task, the chief minister said.
Karnataka has reported around 9.61 lakh COVID-19 cases and over 12,000 deaths so far.
(With inputs from PTI)