According to preliminary results released by the UK media, the Conservatives sustained losses in many regions.
"Leaving with the good deal we've negotiated, a deal that works for the UK is the very best possible outcome. And it's a price worth striving for. We need a Brexit that works for our manufactures and our exporters, that keeps supply chains flowing and opens up new routes for trade, and our deal does that. Leaving with no deal would not," May said at the Welsh Conservative conference in the Welsh town of Llangollen.
She stressed that the United Kingdom needs a Brexit deal that works for "the police officers fighting crime across borders and security agents using shared intelligence to defeat terrorism."
"Our deal does that, and leaving with no deal would not… Our goal is to deliver Brexit so that we could move our country forward and I will keep fighting and we must all keep fighting to achieve that goal," she added.
The prime minister warned that exiting the 28-nations bloc without an agreement could risk the unity of the United Kingdom.
"Majorities in two nations of our United Kingdom voted to leave, majorities in the other two voted to remain. In Northern Ireland there's the added challenge of a land border with the EU. So we need a Brexit that works for the whole of the United Kingdom, and our deal does," she said.
May admitted that there was a difficult time for her Conservative party and the results of the recent local elections are "a symptom of that."
"We have the responsibility to deliver something truly historic. What is momentous and historic is seldom simple and straightforward but I think there was a simple message from yesterday’s elections to both us and the Labour Party: Just get on and deliver Brexit," she concluded.