Scotland voted against independence in 2014, but voted to remain in the European Union in 2016 while the United Kingdom as a whole voted to quit the bloc. Sturgeon says this means Scotland should have another chance to vote on secession.
"If the SNP wins this election in Scotland and the Tories (Conservatives) don't, then Theresa May's attempt to block our mandate to give the people of Scotland a choice over their own future when the time is right will crumble to dust," Sturgeon, who heads Scotland's devolved government, told reporters in London.
Polls suggest Scots do not believe the timing is right for another referendum, although support for independence itself has been broadly steady at around 45 percent or more, and the SNP is predicted to win most Scottish seats in the snap poll.
Scottish Conservative leader Ruth Davidson says the election will show the SNP is now "going downhill".
The issue of the SNP's mandate is likely to dominate the June 8 election in Scotland after Theresa May told Sturgeon that now was "not the time" to discuss independence with the shape of Britain's relationship with the EU yet to be decided.
However Sturgeon shot that argument back at May, pointing out that the prime minister was calling a national election despite having previously insisted it would be the wrong thing for the country.
Sturgeon said May was putting Conservative interests before those of the country by trying to capitalize on the weakness of the main opposition Labour Party to push through her own agenda.
"(May's) motive is clear. She knows that as the terms of her hard Brexit become clearer, the deep misgivings that so many people already have will increase and grow. So she wants to act now to crush the parliamentary opposition that she faces," Sturgeon said in a statement.
The SNP currently has 54 of Scotland's 59 seats in the British parliament in Westminster. May's Conservatives, which had their lowest share of vote in Scotland in a general election in 2015, have just one.
May enjoys a huge lead in opinion polls over the main opposition Labour Party, and the British economy has so far defied predictions of a slowdown, offering her a strong base to win the nationwide vote by a large majority. Scotland is expected to produce a completely different result from England.