Theresa May has called on voters from both sides of the EU debate to back her in next week's general election to "fulfil the promise of Brexit".
In a bid to focus on Brexit after being criticised for avoiding a TV debate, she said it could bring "enormous" opportunities.
She said Labour's Jeremy Corbyn was "not up to the job" of managing it.
But Mr Corbyn accused the Tories of creating a "toxic climate" in EU talks, using "hectoring and threats".
And the Lib Dems said the PM's "hard Brexit" approach would harm the economy.
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Mrs May used a high-profile speech to set out her vision of European Union withdrawal as part of a "great national mission" to build a "stronger, fairer and more prosperous Britain".
With just a week to go to the election, the prime minister said this future could only be delivered if voters backed the Conservatives when they went to the polls on 8 June.
In a speech in Teesside, she said: "If they do, I am confident that we can fulfil the promise of Brexit together and build a Britain that is stronger, fairer and even more prosperous than it is today."
She said Brexit offered huge opportunities to build a "Britain beyond Brexit that is more global and outward-looking. A Britain alive with possibilities, more confident in itself, more united and more secure.
"A country our children and grandchildren are proud to call home.
"If we get Brexit right, we can be a confident, self-governing country once again.
"A country that takes the decisions that matter to Britain here in Britain."
She said it was time to "respect the decision of the British people" to leave the EU and said she was ready to do so "from day one". But she claimed Labour leader Jeremy Corbyn was "simply not up to the job".
"He doesn't believe in Britain. He doesn't have a plan. He doesn't have what it takes.
"And after last night it's clearer than ever that just 11 days after the election when the negotiations begin, Jeremy Corbyn's focus wouldn't be on trying to negotiate a deal for Britain in Europe, but on trying to stitch up a deal with [SNP leader] Nicola Sturgeon and the rest."
BBC assistant political editor Norman Smith said there was a more optimistic, confident tone about what life would be like post-Brexit in Britain as the prime minister sought to give people a sense of better times ahead, following a campaign dominated by talk of "hard choices" and "huge challenges".
In his own speech on the same subject later, Mr Corbyn accused the Conservatives of putting jobs at risk and backing a plan that threatened to turn the UK into an "low-wage, offshore tax haven".
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He told supporters: "So far the rhetoric and threats from the Tory government has fostered a toxic climate. Labour will start negotiations by setting a new tone.
"We will confirm to the other member states that Britain is leaving the European Union, that issue is not in doubt, but instead of posturing and pumped-up animosity, a Labour government under my leadership will set out a plan for Brexit based on the mutual interests of both Britain and the European Union."