But he said he recognised that he would not "be able to give the effort, energy and complete focus needed at this important time" and therefore believed that "the right thing at this time is for me to stand down from my current responsibilities".
Mrs May, who carried out a cabinet reshuffle on Monday, joined those in paying tribute to Mr Brokenshire and wished him a "speedy recovery".
That has resulted in a unprecedented purgatorial existence for Northern Ireland where there is no government but civil servants continue to run public services and either take political decisions or leave key decisions untaken. The former Deputy First Minister's resignation over Arlene Foster's refusal to step aside as First Minister over the cash for ash scandal brought down the Stormont Assembly.
A government source says he will be citing "ill-health", which will be confirmed in an official letter to the British Prime Minister this morning.
Her schedule today also includes face-to-face meetings with the leaders of the DUP and Sinn Féin.
Judge blocks Trump from rescinding DACA
Trump's promise to build a wall along the Mexican border was a central tenet of his campaign for president. President Donald Trump says the USA court system is - in his words - "broken and unfair".
Attorney General Rescinds Obama-Era Marijuana Guidelines
Under the state's medical marijuana law enacted in 2014, NY has 1,384 medical practitioners and 40,286 certified patients. Obama-era guidance gave low priority to prosecutions of medical marijuana dispensing under state law.
Nokia 6 (2018) may be unveiled today; here're the key features
Other regions are likely to get it by February as well, but we're not convinced the smartphone will make it to the Americas. The device boots up to Android 7.1.1 Nougat and sports a 5.2-inch Full-HD IPS display with 2.5D curved Gorilla Glass atop.
A Black Widow movie is closer than it's ever been
There's more great news because The Wrap reports that Jac Schaeffer is set to write a script for a Black Widow standalone movie. Johansson has been portraying the life of Black Widow since she was featured in the 2010 film, " Iron Man 2 ".
Alexa will be in your new Toyota, Lexus auto by 2019
Companies are rushing to incorporate voice control into their products and making sure they work with whatever service you use. He doesn't believe having a TV with Google Assistant will dissuade consumers who have Amazon Echos with Alexa in their homes.