But opponents insisted that a vote for the Nationalists will lead to "years of division."
Ms Sturgeon clashed with Tory interim leader Jackson Carlaw at First Ministers Questions today, for the first time since Ruth Davidson stood down.
"First Minister, we respect the results of all referendums, you should give it a try," Mr Carlaw said.
"Perhaps there is one thing we can agree on, that it may now require a general election to sort this out.
"Scottish Conservatives will stand up for and stand by our decision to remain within the United Kingdom - to back the decision people made across the UK to leave the European Union, so ensure this country can move on.
"If you want more years of division, vote for Nicola Sturgeon.
"If you want to get back to the things that matter - schools, jobs, police, the peoples' business, vote for us.
"That is the clear choice that Scotland now faces."
Prime Minister Boris Johnson is seeking to hold a snap election on October 15 after suffering defeat over his Brexit plans in the Commons, but this is being resisted by opposition parties. It appears that an election could now be held in November.
The First Minister added: "She can't stomach the direction Boris Johnson is taking this country in. Boris Johnson's own brother can't stomach the direction he's taking the Tories in.
"The question is why should the people of Scotland be forced to put up with it.
"I relish the prospect of a general election - I really relish the prospect of a general election. The SNP will beat the Tories in a general election, just as we have done in the past number of elections.
"And unashamedly, unapologetically, the message from the SNP will be clear. We stand up for Scotland's opposition to Brexit. And we stand up for Scotland having the right to choose our own future, not having a future imposed on us by Boris Johnson."