Scottish Tory leader Ruth Davidson has warned Theresa May that the party must tone down the hardline approach to Brexit after the election setback.
The reports were seen as a sign that the party's Scottish leader was seeking to assert the influence of her MPs.
Davidson is an increasingly important voice in the Conservative Party.
Scotland's Finance and Constitution Secretary Derek Mackay, who directed the SNP's election campaign, told the same programme: "The First Minister has said that she'll reflect on the result but the fact that another Tory government that Scotland has not elected will rule over us with policies that Scotland just doesn't support I think has been another lesson on why Scotland should have a choice".
She added: "Folk might remember I fought a leadership election on the other side of that particular argument".
The Scottish Daily Telegraph's editor Alan Cochrane said: "The story was impeccably sourced and I stand by every word".
Speaking at her Bute House residence in Edinburgh about her referendum demand, Ms Sturgeon said: "We will reflect on these results, we will listen to voters and we will consider very carefully the best way forward for Scotland, a way forward that is in the interests of all Scotland".
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He also said Ms Davidson was "absolutely not" interested in a move to Westminster despite being tipped as a future leader of the United Kingdom party, insisting that she was "totally focused" on becoming First Minister of Scotland in 2021.
Many commentators focused on the DUP vetoing the introduction of same-sex marriage in Northern Ireland in 2015, in opposition to the rest of the United Kingdom, and in stark contrast to this country which voted in favour of same-sex marriage in a referendum.
Ruth Hunt, chief executive of Stonewall, said the charity was "deeply anxious" about any DUP involvement in the new government given the party's poor record on LGBT rights.
They are opposed to LGBTI equality at large and have been holding up same-sex marriage in Northern Ireland, although there is a majority for it.
"The Prime Minister has made it clear it is her duty to get on with the job in hand and I support all efforts to do so", she said.
"At the same time we must in my view seek to deliver an open Brexit, not a closed one, which puts our country's economic growth first".
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