"Another independence referendum would continue the political stagnation that Scotland has seen for the last decade".
In his letter to Ms Sturgeon, the PM said he had "carefully considered" the arguments she made.
However, Johnson has now written to Sturgeon officially refusing her request for powers over referendums to be transferred to Holyrood. "The people of Scotland voted decisively on that promise to keep our United Kingdom together", he said in the letter today.
The Prime Minister said: "The British government will continue to respect the democratic decision of the Scottish people and the promise you have made to them".More news: Wilder, Fury vow to settle rematch with a knockout
As things stand, a referendum can not take place without the consent of the United Kingdom government.
This would allow the Scottish Parliament to stage separation votes whenever it wants, allowing the First Minister to stage a third referendum if she lost again. They know that given the choice the overwhelming likelihood is the people will choose the positive option of independence. The SNP will be hoping to secure a majority or at least return a pro-independence majority combined with the independence-supporting Scottish Green Party.
Responding to Mr Johnson via Twitter, the SNP leader said: "The problem for the Tories is the longer they try to block democracy, the more they show the Westminster union is not one of equals and fuel support for independence".
The renewed push for Scottish independence was a key policy for the SNP at last year's general election, and although Johnson's campaign was overwhelmingly fought on Brexit, his stalemate with Sturgeon now threatens to damage his leadership, YouGov researcher Chris Curtis told 9News.com.au.
"The question is often posed to me: "what will you do if Boris Johnson says no?"More news: Vic dad dies after NZ volcano eruption
"The ball's in Sturgeon's court, and it leaves the SNP in quite a hard position", said Simon Pia, a former Scottish Labour press adviser.
In the House of Commons, Mr Johnson has regularly blocked SNP MPs' calls for a second referendum.
Harvie commented: "In 2014 the all-party Smith Commission accepted that nothing prevented Scotland becoming an independent country if the people of Scotland chose that path".
"The Westminster union can not be sustained without consent".More news: Scientists say seven billion year-old stardust is oldest solid material found