The Scottish Tories criticised Ms Sturgeon’s “eager embrace of Michelle O’Neill and Sinn Féin”.
Ms Sturgeon said the pair discussed the cost-of-living crisis and the “extremely concerning announcement by the UK Government” that it intends to unilaterally “dis-apply” parts of the Northern Ireland Protocol, which has created economic barriers on trade between Great Britain and Northern Ireland.
The First Minister said this would have “incredibly damaging effects” in communities across the UK, adding: “In a cost-of-living crisis and teetering on the edge of recession, pitching us into a trade dispute with the EU could be what tips us over.
“Intergovernmental relations are essential when it comes to tackling shared challenges and it is clear that much more needs to be done by the UK Government to ensure a rapid and effective response to the devastating cost-of-living crisis facing households across these islands.
"No one should ever have to make a choice between heating and eating.
“Today’s meeting was a further example of the close relationship between Scotland and Northern Ireland.
"In that spirit, I have written today to the leaders of the DUP and Alliance parties with an offer to meet to discuss these important matters.”
Ms Sturgeon told Bauer Media it “matters to Scotland what happens around the Northern Ireland Protocol”, adding: "Because if we do see the UK Government, as it is threatening to do, take unilateral action – if that, as it may well do, prompts a trade war between the UK and the EU – that will have significant and very severe impacts on Scotland, on our businesses and on living standards for individuals.”
After the meeting, Ms O’Neill tweeted: “Delighted to meet Scotland’s First Minister @NicolaSturgeon in beautiful Edinburgh.
"The historic bonds between Scotland & the island of Ireland go back centuries. We enjoy a long & enduring affinity as neighbours & friends.
"Moving forward we will strengthen the bonds that tie us.”
It came as political leaders in Northern Ireland met Irish premier Micheal Martin in Belfast as the deadlock at Stormont continues.
The DUP is blocking the re-establishment of Stormont’s power-sharing institutions in protest at the protocol.
Ms O’Neill, whose party won the most seats at the recent election in Northern Ireland, has accused the DUP of “denying democracy” by refusing to enter government.
Scottish Conservative MSP Donald Cameron said: "People across Scotland, including those who support independence, will be concerned about Nicola Sturgeon’s eager embrace of Michelle O’Neill and Sinn Féin.
"For many, the party’s associations will be far from the ‘civic nationalism’ that Nicola Sturgeon claims to champion, but it seems that the SNP will work with anyone so long as they support the break-up of the UK.
"It's important to remember that in every intervention the SNP makes, it does so with the intention of only one selfish and damaging goal."