The Prime Minister, prior to her Monday meeting with Ms Sturgeon, told the Scottish First Minister she would not sanction a second vote until Brexit is complete.
Scottish lawmakers have backed calls by Scotland's First Minister Nicola Sturgeon for a second independence referendum to separate from the United Kingdom, just one day before London triggers two years of negotiations on withdrawing from the European Union.
Speaking on the economic case fought on during the referendum, Gordon MacIntyre-Kemp, founder and director of Business for Scotland said: "Business for Scotland welcomes today's vote in Holyrood to seek a Scottish referendum on independence".
About 62% of Scottish voters backed the United Kingdom remaining part of the European Union in June 2016 and the SNP manifesto for last year's Holyrood elections made clear another ballot on independence should take place if there were a "material change in circumstances" from the previous ballot in 2014.
MSPs voted by 69 to 59 in favour of seeking permission for a referendum before Britain leaves the EU, BBC reported.
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Asked about what would happen if her call for another referendum was formally rejected, Ms Sturgeon said: "I will set that out in due course".
But following her talks with the Prime Minister, Ms Sturgeon said it was "very difficult" for her to maintain a "rational opposition" to a referendum on her timetable.
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Conservative leader Ruth Davidson also hit out at the proposal for a second vote, saying most people had no desire for another "divisive" referendum.
She reiterated that it was "not the time" for the Scottish referendum and that it would be unfair to voters to decide on something before all the facts of Britain's terms of exit from the European Union were known.
He said the deal should ensure a strong, collaborative future relationship with the EU; it should deliver "the exact same benefits" Britain now enjoys as part of the single market and the customs union; it should ensure the fair management of migration; it should defend workers' rights and protections; it should protect national security and cross-border co-operation on crime; and it should deliver for all regions and nations of the UK.
But May said in a speech to aid and development officials in East Kilbride that "Now is the time when we should be pulling together, not hanging apart".
The first minister is now expected to make the formal request for a section 30 later this week - after May formally starts the Brexit process on Wednesday by triggering Article 50.
May's London-based government would have to approve a legally binding referendum, and May says "now is not the time" for a new independence vote.
May has repeatedly said that "now is not the time" for another independence ballot.
Both May and Sturgeon said they were not ready to compromise and the rift is unlikely to end before Article 50 is triggered.
She will say: "And on that foundation, we have built a country where we share the challenges that we face, and bring all the expertise, ingenuity and goodwill we share across this anon to bear to tackle them".