Nicola Sturgeon has warned that the pandemic is accelerating again as she followed Boris Johnson to impose a “rule of six” on gatherings in Scotland.

Sturgeon said that the new limit of six people from two households would apply both indoors – in houses, in pubs and restaurants – and also outdoors including in private gardens. She added that she hoped this would both reduce transmission and also simplify the rules as much as possible.

She added that she was asking people to follow the revised limit immediately. Any children under 12 who are part of the two households meeting will not count towards the six-person limit, while there will be exceptions for organised sports and places of worship.

In her statement to Holyrood on Thursday, Sturgeon also introduced rules on face coverings, which she said were designed to help keep the hospitality sector open.

The Scottish government will make it mandatory for customers in hospitality premises to wear face coverings whenever they are not eating or drinking, for example arriving, leaving and when visiting the bathroom. It will also be mandatory – rather than simply guidance – for staff working in hospitality premises to wear face coverings.

Sturgeon told MSPs that the country was not ready to move to phase 4 of her government’s routemap out of lockdown, as she confirmed an additional 161 cases of Covid-19 since Wednesday, with 65 of those in Greater Glasgow and Clyde, where five local authority areas are facing additional restrictions on indoor gatherings.

Further re-openings have been delayed until 5 October, including sports stadia, theatres, live music venues, indoor soft play facilities and indoor contact sports activities for people aged 12 and over.

Sturgeon also urged the public to download the Protect Scotland contact-tracing app, which was launched on Wednesday evening. The app adds to the current test & protect system, providing notifications if someone you have been in close proximity with tells the app that they have tested positive.

She said that this would be particularly useful for settings – such as public transport – where people spend time in close proximity to people they don’t know.

Sturgeon also addressed the fact that many of the new infections are among younger people, which she said partly explained why recent rise in cases had not been mirrored by an equally large rise in hospital admissions or deaths.

She said: “Although that can provide some comfort, it should not lead to complacency. Although Covid kills relatively few younger people, we know it can still be harmful to their health. It is not a virus anyone should be relaxed about getting.”

But Sturgeon added that it was important not to blame younger people for the infection rise: “I understand how hard this is for young people and it is not their fault. Younger adults are more likely to work in public-facing jobs, more likely to have to use public transport and live in shared accommodation.”