Ms Sturgeon, alongside the First Minister of Wales Mark Drakeford, have both offered for their governments to become “super sponsors” for Ukrainian refugees coming to the UK.
Scotland has offered sanctuary for 3,000 refugees, mirroring the offer made for the Syrian Refugee programme, with the Welsh Government offering this for 1,000 refugees.
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At Parliament on Monday, Michael Gove said the UK Government would “work closely” with the devolved nations “to make sure their kind offers of help are mobilised”.
A Scottish Government spokesperson said: “If needed, the First Minister would be willing to play her part in offering refuge.
"Ministers are still pressing the UK Government to go further and faster on accepting refugees fleeing Ukraine, but do not yet have the details from them on how a scheme will work, and what scope there may need to be for asking individuals or families to provide a shelter.”
It comes as there have been over 44,000 applications to Homes For Ukraine within five hours of UK Government site launch.
The Homes for Ukraine scheme will enable individuals, charities, community groups and businesses in the UK to bring Ukrainians to safety, including those with no family ties to the UK.
The website allows UK individuals, charities, community groups and businesses to record their interest in supporting Ukrainians fleeing the war through the scheme.
Mr Gove announced the Homes for Ukraine scheme would have “no limit” for those who can benefit from the scheme.
However, the scheme will initially facilitate sponsorship between people with “known connections”, according to Mr Gove.
Under the scheme, Ukrainians will still need a visa to access the UK.
Europe minister James Cleverly said of the support: “The generosity of spirit displayed by everyone in the UK with regard to their willingness to host Ukrainian refugees has been fantastic.
“We have tried to make sure the system is as quick and as smooth as possible and that includes making sure people can retrospectively apply for visas.
"Nearly 10,000 people an hour are signing up to the site which is absolutely fantastic.”
It is understood that at one point so many people logged onto the site that it crashed the system.
Almost three million people have fled Ukraine since Russia invaded.
Mr Cleverly said it was not clear how many refugees wanted to come to the UK in comparison to the numbers who wanted to “stay close to their homes” in neighbouring countries.
Talks have resumed on Tuesday morning between Russian and Ukrainian negotiators.
Mr Cleverly said: “Russian leadership under Vladimir Putin must realise that the attack he thought was going to be so easy has proven to be anything but easy.
"I really hope these talks are fruitful, but we will judge Russia by its actions and what we want to see is, of course, to see Russia leave Ukraine.”