The Conservative leader said she wanted the "best possible deal" for Wales and the whole of the UK.
Meanwhile, Mrs May said the issue over whether ex-UKIP AM Mark Reckless sits with the Conservatives in the Senedd was a matter for the assembly group.
Her comments came after Labour denounced her visit to the party's Welsh heartlands on Tuesday as a stunt.
Speaking to BBC Radio Wales' Good Morning Wales, Mrs May said: "I want not only to get the best possible deal for trading with the European single market for the future, for businesses, for farmers, for Wales and the whole of the United Kingdom.
"I also want to see us opening up new markets across the rest of the world for people here in Wales to be trading with.
"Every vote here in Wales and across the UK for me and the Conservatives will be a vote that strengthens my hand in those important negotiations," she told the programme.
Prior to the announcement of the 2017 general election, a row was sparked within the Conservative party when Mark Reckless left UKIP and joined the Welsh Conservative group as an independent.
Asked if she had confidence in Andrew RT Davies' leadership, Mrs May replied: "Andrew Davies is the leader of the Welsh Conservatives in the Welsh Assembly."
Speaking for the first time about the row, she added: "Andrew Davies has been doing a good job in the Welsh Assembly. It's their decision as to who sits with them.
"Mark Reckless is an independent member of the Welsh Assembly."
On Tuesday, Welsh Labour leader and First Minister Carwyn Jones said Mrs May's decision to visit Labour heartlands in Wales was a "stunt".
He said what was important was that people "see the Tories for what they are, their idea of leadership is to say nothing and do nothing".
"What we want is to offer hope," he said, "to say to people it doesn't have to be this way".
Plaid Cymru MP Jonathan Edwards said: "You have to travel 1000km across Europe to find a poorer place than West Wales and the Valleys - that is the legacy of the Tories in government.
"The Conservatives have never, and will never, operate in the best interest of Wales, and with Labour too weak and divided to challenge them, it is left to Plaid Cymru to fight for the best possible Brexit deal for our country."
Prime Minister Theresa May has said she wants to open new markets for Welsh businesses to trade following Brexit.