The Prime Minister is adamant her position "will not change" with regard to Scottish independence, saying Brexit is more important.
After smiling for the cameras with her Scottish counterpart, Mrs May disappeared for critical talks with the First Minister.
Earlier, she said: "My position is very simple and it hasn't changed.
"It is that now is not the time to be talking about a second independence referendum and that's for a couple of reasons.
"First of all, now is the point when we are triggering Article 50, we're starting negotiations for leaving the European Union. Now is the time when we should be pulling together, not hanging apart. Pulling together to make sure we get the best possible deal for the whole of the UK.
"Also I think it would be unfair on the people of Scotland to ask them to make a significant decision until all the facts were known, at a point where nobody knows what the situation is going to be.
"My position isn't going to change, which is that now is not the time to be talking about a second independence referendum."
Live pictures: May meets Sturgeon during visit to Scotland Mon, March 27, 2017
British Prime Minister Theresa May met Scottish First Minister Nicola Sturgeon in Glasgow, following the announcement that Scotland is to hold a second Independence Referendum
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Shoes worn by Prime Minister Theresa May during a speech at the Department for International Development's office at Abercrombie House in East Kilbride during her visit to Scotland
Mrs May also vowed to "forge a more global Britain", days after slapping down Scottish First Minister Nicola Sturgeon’s demands for a independence referendum before Brexit.
She also promised "a more united nation", despite increased calls for independence in Scotland and Irish unity in Northern Ireland following last year's Brexit vote.
Speaking at the East Kilbride base of the Department for International Developmen this lunchtime, Theresa May said: "I want to make it absolutely clear that this is not in any sense the moment Britain steps back from the world. We are going to take this opportunity to forge a more global Britain…to build relationships with old friends and new allies alike."
She vowed to push for a kind Britain that would remain connected with the wider world.
Mrs May said: "The work you do here in conjunction with your colleagues says something important about Britain.
"It says we are a kind an generous country, it says we are a big country that will never let down or turn our back on those in need.
"We will always meet our commitment to the world."
Theresa May laughs off Nicola Sturgeon's demands for a second Scottish independence referendum
The pair met alongside representatives inside the Galsgow Crown Plaza Hotel
That is why the plan for Britain I have set out has at its heart one overarching goal – to build a more united nation
She also said she would bring Britain closer together in the following vital weeks and months.
Mrs May said: "When this great union of nations, England, Scotland, Wales and Northern Ireland, sets its mind on something and works together with determination we are an unstoppable force.
“That is why the plan for Britain I have set out has at its heart one overarching goal – to build a more united nation. I believe when we work together there is no limit to what we can do.
Theresa May said Britain will continue to be a 'force for good'
"A more united nation means working actively to bring people and communities together by promoting policies which support integration and social cohesion.
"In Scotland, Wales and Northern Ireland that means fully respecting, and indeed strengthening, the devolution settlements.
"But never allowing our Union to become looser and weaker, or our people to drift apart.
She said, rather than destabilise Britain, Brexit would lead to a closer bond between England, Scotland, Wales and Northern Ireland.
The Prime Minister said: “As Britain leaves the EU and we forge a new role for ourselves in the world, the strength and stability of our union will become even more important.
"This proud shared heritage provides the bedrock of our lives in the UK.
"As we face this great national moment together I hope you will continue to play your part to build a stronger Britain, a more united Britain that I’m determined we shall be once we emerge from this period of national change.”
“This United Kingdom and its values at its heart is one of the greatest forces for good in the world today and when we work togetherr and set our hearts on a task we really are an unstoppable force.”
This is an ongoing story. Check back soon for more information.