Mrs May looked to capitalise on many Labour supporters’ uncertainty over leader Jeremy Corbyn by presenting the June 8 poll as a vote on who will be Prime Minister rather than which party will be in government.
Signalling the Conservatives’ growing ambitions in next month’s election, Mrs May delivered her message on the fringes of Leeds North East, a constituency held by Labour since 1997 where sitting MP Fabian Hamilton is defending a majority of more than 7,000.
A swing big enough to secure Leeds North East would point to the Conservatives also taking Labour-held seats including Wakefield, Halifax and Dewsbury.
Mrs May said: “I know that this is a city, it’s a place where perhaps people usually might say that it’s a traditional Labour area but here and in constituencies across the country although it may say Labour on the ballot it will be Jeremy Corbyn who gets the votes.
“There are only two people who it is possible will be prime minister on June 9, only two people who can possibly represent Britain in Europe and the choice is between five years of strong and stable leadership with me as prime minister or a coalition of chaos with Jeremy Corbyn at the helm, a weak leader negotiating Brexit.
“Higher taxes, more waste, more debt.”
She continued: “In this election every single vote will count. Every person in this country has a positive reason to lend me their vote.
“Because this election is not about who you might have voted for in the past, it’s about voting in the national interest, it is about voting for the future."
Opinion polls giving the Conservatives a significant lead over Labour have encouraged the party to shift away from the focus of its last election campaign on a string of West Yorkshire seats taken from Labour in 2010.
Those seats are now considered relatively safe and the party has shifted its sights to constituencies where Labour MPs only secured narrow victories last time and those where large numbers of people voted Ukip in 2015 and could switch this time around.
Mrs May used her speech at the Shine centre in Harehills to ramp up the rhetoric over the forthcoming Brexit talks, referring to comments made by German Chancellor Angela Merkel that there were people in Britain with “illusions” about the process.
The Prime Minister told the audience “there will be times when these negotiations are going to get tough” and “27 other countries are lining up to oppose us”.
Mrs May said she wanted to make a “simple pledge”.
“That if you vote for me to strengthen my hand at the negotiating table in Brussels, I will do everything I can to represent the interests of every person in this great city and every person in our great country.”
Mrs May said the Conservatives had a “positive message and will fight a positive campaign”.
“Give me a mandate to lead Britain, give me a mandate to speak for Britain, give me a mandate to fight for Britain and give me a mandate to deliver for Britain."
Rachel Reeves, Labour MP for Leeds West, said: “Theresa May has been Prime Minister for nine months, yet this is the first occasion in all that time she’s bothered to come to Yorkshire.
"People here aren’t fools – she can’t just rock up at election time and demand their vote after completely neglecting our area throughout her time in office.
“In my constituency alone the school cuts her Tory government’s planning will mean 100 fewer teachers. Our A&E departments have patients waiting hours on trolleys. Nestle in York is losing 181 jobs as we start to feel the impact of the extreme Tory Brexit – why isn’t she there trying to do something about that?
“The people of Yorkshire have never needed strong Labour voices to stand up for them in parliament more than they do now.”