The Scots Tory leader today ruled out any prospect of running for Westminster and challenging for the United Kingdom leadership, insisting she is "100%" behind Mrs May.
Ms Davidson has said she has received assurances from the Prime Minister over gay rights should the Tories do a deal with the Democratic Unionist Party, and has urged Mrs May to put the economy first by pursuing an "open" Brexit.
The Scottish Daily Telegraph's Alan Cochrane said: "The story was impeccably sourced and I stand by every word".
The DUP and Conservative party will work together in the coming days to strike a policy pact.
Asked if Scottish Tories would push for a softer line on Brexit, he said: "I think we can have a tremendous amount of leverage".
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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.
The DUP opposes same-sex marriage and Northern Ireland is the only part of the United Kingdom where it is not legal.
In an early indication that she might seek a greater influence in the United Kingdom party, Ms Davidson said on Friday she had been given assurances that any Conservative deal with the Democratic Unionist Party (DUP) would not affect LGBTI rights.
She tweeted that she fought a leadership campaign opposing the idea of a separate organisation in Scotland.
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.
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"A party that constantly misuses its veto in this way is not a party that shares Stonewall's values or the values of most people across the United Kingdom", she said.
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.
Carmichael, who was chair of parliament's education committee and a vocal proponent of soft Brexit, also feared how a rightwing coalition would impact on European Union talks.
"Hard Brexiters have got some thinking to do - a minority government with the stresses and strains of coalition - may be a short-lived affair", he added.
That put them ahead of Labour and closed the gap to the SNP - who had a awful night, losing 21 seats including their Westminster leader Angus Robertson and former Scottish First Minister Alex Salmond.
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