John Swinney said that despite current measures, the virus “does not show much sign of abating”, which means further measures may be needed.
He said the country was facing a “very alarming situation” after recording its highest death toll so far in the pandemic in the past two days – with 93 dead.
Professional sports, as well as manufacturing and construction work were allowed to continue in this lockdown, despite not being in the first wave in March.
The deputy premier said the landmark cabinet meeting on Monday saw ministers question whether they had gone far enough to stop the spread.
Mr Swinney told Politics Scotland: “I don’t think I am revealing a state secret when I say that the debate in Cabinet was not whether we were going too far but whether we were going far enough. ”
To illustrate the rise, Mr Swinney said Scotland recorded around 130 cases per 100,000 people on Boxing Day, but that figure rose to 300 just 10 days later.
Despite the new measures put in place, Mr Swinney said: “It shows no signs of slowing down.
“We are seeing case numbers hovering around 2,000 per day… so we have a situation that is accelerating and we have to constantly consider whether further restrictions are needed.
He added: “We remain open to consider further restrictions if they are necessary. ”
Prime Minister Nicola Sturgeon said on Thursday she could not rule out tougher measures either, after the number of people hospitalized in Scotland surpassed the April peak of the pandemic.
During the coronavirus briefing in Edinburgh, she said: ‘For this lockdown to really be as effective as we need it to be, we need to drastically reduce the number of interactions we have, and that means minimizing when people are forced to leave. Their houses.
“If we’re going to demand the shutdown of more non-essential activities to achieve this, we will have to.” This is an issue the Scottish government is currently examining. ”