"It looks as if it is beyond any doubt that there will be a pro-independence majority in that Scottish parliament", Sturgeon said.
The Scottish National Party itself is seen falling just short but with the support of the pro-independence Green Party, they will have a majority on that issue.
The British government says that legally Scotland needs permission from the British Parliament to hold a referendum.
Scotland held a vote on independence in 2014, billed as "once in a generation", in which just over 55% voted to remain part of the UK.
He said it would be a "difficult journey" and added: "The broad shoulders of the United Kingdom have supported jobs and businesses the length and breadth of the country, but we know that economic recovery will be a serious shared responsibility".
"If Boris Johnson or whoever is Prime Minister at the time, has any respect for Scottish democracy, they will come together with the Scottish Government as happened in the run up to 2014 and agree (to allow a referendum)", said Sturgeon, adding it would be for the United Kingdom government to make a legal challenge.
The sets the scene for a bitter clash between the Scottish government in Edinburgh and Johnson's United Kingdom-wide administration in London, which could ultimately lead to the end Scotland's 314-year union with England and Wales.
"I think a referendum in the current context is irresponsible and reckless", Mr. Johnson told the Daily Telegraph in an interview published on Saturday.
The Scotland results have been the main focus since an array of local and regional elections took place Thursday across Britain, in which around 50 million voters were eligible to vote.
There was also limited tactical voting on the pro-independence side, with the Greens increasing their seats from six to eight, meaning a majority of MSPs will still be in favour of breaking up the UK.
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"But in some of the big ballot boxes, I think we ended up over 3% in Aberdeenshire East, the same in Banff and Buchan, a bit more actually, which I'm pleased with because these are our best results in Scotland".
Recent polls suggest "no" would win again in an immediate referendum, as many fear further upheaval post-Brexit.
In England, the Conservatives registered significant gains in council elections and mayoral races in England, embarrassing Labour.
It became apparent that the tactic had succeeded in denying Ms Sturgeon an overall majority of 65 after it was confirmed that the Tories had held on to the key seat of Aberdeenshire West - where the First Minister made multiple campaign visits - thanks to a 10 per cent swing to the Conservatives from the LibDems.
Johnson said the vote was "very encouraging" for his government, while Starmer said he was "bitterly disappointed".
A similar invitation to the summit was being sent to Northern Ireland's first minister and deputy first minister, Mr Johnson said.
Voters went to the polls on Thursday to decide the makeup of the Scottish and Welsh parliaments, as well as the mayors of England's largest cities, including London and Manchester.
Mr Johnson said the United Kingdom needed to "show the same spirit of unity and cooperation that marked our fight against the pandemic" in ensuring the Union recovers from COVID-19.
Sky News suggested the Tory results were down to a "Boris bounce".
He touted government economic support during the pandemic and the vaccine drive.