Scotland’s health secretary, Humza Yousaf, has said it will be “extremely challenging” to hit the new Covid booster target and confirmed there would be new controls to stem the spread of the Omicron variant.

Yousaf said the health service would need to draft in medical students, army personnel and private contractors, and switch NHS staff from normal duties, to have a chance of hitting the new target of boosting all eligible adults by the end of January. He said some non-essential operations may need to be postponed.

“It will be extremely challenging and that’s why we’re going to have to strain every sinew we can [and] that includes potentially having to move NHS staff away from other core duties to do this,” he told BBC Radio Scotland.

In her statement on Sunday evening confirming the Scottish government supported the revised booster target date, Nicola Sturgeon hinted that it could be hard to achieve. Describing the new date as “the aim”, the first minister said it would be met “if possible”.

Yousaf said it was “inevitable” the first minister would announce fresh restrictions to combat the rapid surge in Omicron infections in an update to the Scottish parliament on Tuesday, after briefing her cabinet that morning.

He would not speculate on what that would involve. He confirmed that closing schools early for the Christmas holidays – a proposal being pushed by the EIS, Scotland’s largest teachers’ union, was being considered but he said that was a measure of last resort.

The first minister had made clear last week she wanted to avoid disrupting schools, partly to support children’s mental health. “We will do everything we possibly can to keep schools open during this period,” Yousaf said.

Although Scotland already has the highest booster vaccinations figure of any UK government, the health secretary added, hitting the target date would mean nearly doubling the daily rate.

As things stand, he said, there were not enough qualified vaccinators to do so. There are already long queues and delays at many vaccination centres, and some walk-in clinics are running out of doses.

Last week, Yousaf had warned it would be very difficult to meet the original booster target date of 31 January, and ministers in Edinburgh had been pressing the Ministry of Defence to release more army personnel to help.

“To ramp up even more from where we are at the moment would require us to go from 40,000 third doses and boosters in a day to somewhere like 70,000. That’s a huge increase that we have to try to get to,” he said on Monday.