Gyms and theatres in Scotland could remain closed for several more weeks in a move designed to ensure children can return to school full-time in August.
Current restrictions - which have also shut non-essential offices - are due to be reviewed next Thursday.
But at her daily briefing Nicola Sturgeon warned the review may not lead to the reopening of more businesses.
She wants to keep the virus at a low level so schools can safely reopen.
In her latest briefing, Ms Sturgeon said she wanted to "inject a note of caution" about the possibility of easing more restrictions next week.
She said the Scottish government's main focus was on "fully and safely" reopening schools on 11 August and removing the requirement for shielding from 31 July.
"These two aims... are really important priorities and, to be frank, they are only achievable if levels of Covid in the community remain very low," she said.
The Scottish government is obliged to review lockdown restrictions every three weeks.
Businesses including indoor gyms, theatres, non-essential offices, call centres and bingo halls are among those due to be considered for reopening as part of the Phase 3 plan.
However, pointing to the Lanarkshire outbreak and the rising numbers of cases in some other countries, Ms Sturgeon said the government needed to be "confident" it was safe to ease restrictions.
The first minister said data would be reviewed and a final decision on lifting more restrictions would not be made until next week.
But she added: "We cannot leave restrictions in place for longer than we judge to be necessary, but I did want to flag up now that it is possible we may not be able to make any changes next week beyond confirming the return of schooling and a pause in shielding.
"And so for those businesses who are still waiting for a date to restart, I want to thank you for your ongoing patience.
"I fully understand how difficult any further delay is for you. I also hope you understand why we need to act safely and cautiously and prioritise the reopening of schools."
Scotland spent three weeks in Phase 2 - when non-essential shops and beer gardens reopened - before moving into Phase 3 on 10 July.
- the tourism industry has reopened
- people have been able to go inside pubs and restaurants
- and hair and beauty salons have thrown open their doors.
The latest statistics from the National Records of Scotland show that deaths from coronavirus have dropped to the lowest level since the start of the pandemic, with just six recorded fatalities last week.