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In a TV interview, he said First Minister Nicola Sturgeon would update the Scottish Parliament next week, but added: “I think you’re right to question that date.”
Mr Yousaf also insisted Scotland had enough supplies to complete the vaccination programme, but would like more so it could go faster.
With Boris Johnson expected to delay the June 21 lifting of all legal restrictions south of the border, Mr Yousaf was asked on BBC One’s Sunday Show if Scotland’s scheduled drop to level zero a week later was now likely to be postponed until August.
He said the Scottish Government had taken the cautious approach, always led by public health data.
“We as a government came under pressure when the UK Government announced their 21 June date to give some sort of indication of similar dates, but we resisted that,” he said.
Mr Yousaf said Ms Sturgeon would update Parliament next week in line with the latest data.
"I don’t have a crystal ball. I think you’re right to question that date because the Delta variant is a bump in the road,” he said.
"It’s important we understand fully the link between positive cases, hospitalisation, severity of illness, how long are people staying in hospital, are they going into ICU
"These are all the questions – and we’re looking not just at one week’s data, but at weeks of data to make sure we have a firm answer before we give the public a decision about what the future is in terms of moving through the levels.”
He was asked, if some areas of Scotland remained in level two, whether dispensation could be made for some sectors such as the wedding industry, where a maximum of 50 are allowed at ceremonies or receptions.
Mr Yousaf said he understood the pressure on a number of sectors, particularly the wedding sector, and knew many people had had to postpone weddings.
“We know how hard hospitality has also been hit, leisure has been hit,” he said.
"We will work with them, but we will always be guided by the public health advice. I can’t promise what differences, if any, there will be at this stage.”
Mr Yousaf wrote to UK health secretary Matt Hancock last week to request the ramping up of supply of the Pfizer vaccine, which is recommended for younger adults.
Asked about supplies, Mr Yousaf said: "We have enough supply to complete our programme – our next milestone will be the end of next month to complete all first doses for the adult population and we’re on schedule to do that.
"But clearly if we have more supply we can go faster. You can do more drop-in clinics, for example.”
He said he had had conversations with Mr Hancock and vaccines minister Nadhim Zahawi and both were “very positive”, adding: "I think all four nations are in the same place around that limit of supply of Pfizer.
"I’m reassured by what Mat Hancock said in terms of the conversations they’re having with Pfizer and the work the vaccines taskforce is doing so we will continue to work together collaboratively to see what we can do to source more supply.”