It comes after the First Minister announced on Tuesday that all adults will have received an appointment notification by the end of next week.
The previous target date for all appointments to be offered was July 31.
The First Minister told a Covid-19 briefing on Friday: “We have indicated all along that we expected to have offered first doses to all adults by the end of July… All appointments for all adults should be with people by the end of next week, so you can see that the programme is going faster than we previously anticipated.
“I'm also pleased to confirm that we now expect to have completed fist doses for all adults by the 18th of July.
“Again, faster progress than we thought might be possible just even a few weeks ago.”
The vaccination programme has recently accelerated in Scotland, with the gap between first and second doses shortened from 12 to eight weeks.
When asked when second doses will be completed, the First Minister said: “Eight weeks from that takes us to mid-September, which is when we would hope that we will be on track to complete second doses.”
She added: “The caveat I’ve got to put in there is that is dependent on us having the supply to do that – but we are wanting to give second doses eight weeks after first doses.
“So if we’re going to complete first doses by the middle of July then eight weeks after that is when – all things permitting – we would hope thereabouts to be completing second doses as well.”
Health Secretary Humza Yousaf said he is “delighted” at the acceleration of the programme.
He said: “I want to stress how important it is that everyone takes up their offer of a vaccine when they get it. The emergence of the Delta variant shows we cannot be complacent, and the vaccination programme – along with restrictions and testing – offers protection to you, your loved ones and your community.”