Nicola Sturgeon is under growing pressure to take major decisions on coronavirus to Holyrood after a backlash over sending students back to campus.
Opposition leaders are increasingly angry at being left out of the loop despite claims the government has to act quickly.
It comes as MPs were denied a vote on having a formal say in future restrictions in England on Wednesday.
Earlier this week, Sturgeon said she will speak to parliament about how to “increase the scrutiny”.
But confusion over decisions being made on reopening universities spilled over into parliament yesterday, with MSPs demanding apologies and more say in setting rules.
Writing for the Record, Scottish Green Party co-leader Patrick Harvie explains why he thinks the minority Scottish Government needs to listen to parliament.
Demands for greater power are not just being heard at Holyrood.
In the Commons on Wednesday, Boris Johnson was accused by the Speaker of treating Parliament with contempt for his handling of new rules on coronavirus.
In a strongly worded statement, Sir Lindsay Hoyle hit out at the "totally unsatisfactory" way Parliament had been sidelined, with new laws being brought in without scrutiny and sometimes published just hours before coming into force.
But Johnson was spared a vote on a rebel Tory bid to require the Government to give Parliament a greater role.
In Edinburgh, the First Minister was asked to open up to the Scottish Parliament during her daily briefing to journalists earlier this week.
Sturgeon said: "In a situation that is fast moving, where we often have to move really quickly to put restrictions in place, of course we want to maximise parliamentary involvement and scrutiny. So we will consider on an ongoing basis the best way of doing that.
"Right now, parliamentary committees can sit on any day to scrutinise any proposals that are put forward, they're not limited to just sitting on parliamentary sitting days.
"We do, particularly six months in, keep this under review and we will want to talk to parties across the parliament about how we increase the scrutiny and have as much of that scrutiny as early as possible, albeit recognising that sometimes, because the virus doesn't wait for parliamentary scrutiny, we have to act quickly."
