"I am sorry that you have chosen to leave the Government when we have already made so much progress towards delivering a smooth and successful Brexit, and when we are only eight months from the date set in law when the United Kingdom will leave the European Union," May said in a letter to Davis obtained by The Guardian.
The prime minister has also thanked Davis for "everything" he has "done over the past two years as Secretary of State to shape our departure from the EU."
"I am sorry that the Government will not have the benefit of your continued expertise and counsel as we secure this deal and complete the process of leaving the EU," May added.
The white paper, May said, will propose a EU-UK free trade zone for industrial and agricultural goods, as well as a common customs territory, putting the cabinet on a collision course with many hardline Brexiters among the ruling Conservatives. The UK government previously was inclined to establish a full-fledged customs union regime with the bloc without any exceptions and with the application of WTO tariffs.
UK Labor leader Jeremy Corbyn believes that Davis' resignation shows the prime minister's inability to implement Brexit.
Davis' resignation was followed by the resignation of his deputy, Brexit Minister Steve Baker and another Brexit Minister Suella Braverman.