Johnson warned Britain was headed for the "status of colony" of the European Union after it leaves in March, and said the Brexit "dream is dying".
"I think that's what a lot of people don't realize", she said.
May said she had chaired a "productive" meeting of her government, unswayed by the resignations of Foreign Secretary Boris Johnson and Brexit negotiator David Davis that rocked the government on Monday.
May is holding a meeting of her new-look cabinet on Tuesday, following a forced reshuffle in the aftermath of the resignations.
"I get along with her very well", said Trump who is to meet May on a visit to Britain after the North Atlantic Treaty Organisation summit.
But former Conservative leader William Hague warned party rebels that voting against the Prime Minister's final deal could result in Brexit being indefinitely delayed or halted altogether.
The trans-Atlantic relationship has had some awkward moments since Trump's election.
The PM told MPs she wanted to recognise the work of the former Brexit secretary on steering through some of the "most important legislation for generations" and the "passion" that the outgoing foreign secretary had shown in promoting a "global Britain to the world".
Trump, answering a reporter's question about whether May would stay in power, said: "That's up to the people".
Leaked Galaxy Tab S4 render reveals the new S Pen
It's possible that the company may unveil its new tablet at the IFA 2018 trade show in Berlin this September. The Note 9 is set to come pre-installed with Android 8.1 Oreo and would be the first Samsung phone to do so.
Meghan Markle's outfit sends message to New Zealand designer
The couple first met with the president of Ireland, Michael Higgins, and his wife, Sabina Coyne, at their residence in Dublin. Meghan paired the look with Paul Andrew heels in black suede, diamond earrings from Birks, and a sleek, center-parted bun.
British Prime Minister Theresa May has met with her Cabinet as she tries to restore government unity after the resignations of two top ministers over Brexit.
Mr Johnson's almost two years as foreign secretary was not without controversy, with the ambitious Tory heavyweight having been accused of undermining Mrs May on more than one occasion - and making headlines for other reasons.
May's proposals for a future European Union relationship after Britain departs from the bloc next March had taken two-years of internal government wrangling to agree, but within 48 hours Johnson and Davis had resigned saying they could not back the plans.
It comes as federal minister Christopher Pyne reassured the United Kingdom that Australia will have a good relationship with the country's new foreign secretary Jeremy Hunt following Boris Johnson's resignation. But, after much speculation, Mr Johnson announced he would not enter the Conservative leadership race when his ally Michael Gove announced he was running.
He said the British position is now "a basis for a real negotiation now and what we haven't had for many months is a clear negotiating position".
Her spokesman said she had welcomed the new members of her cabinet and they had discussed the publication of a white paper policy document on Britain's future ties with the European Union and stepping up preparations for any no-deal outcome to the negotiations with Brussels.
He was widely reported to have told the Chequers meeting on Friday that putting a positive gloss on Mrs May's Brexit package would be like "polishing a turd", though he later joined other ministers in signing up to the package.
The foreign and Brexit secretaries have both quit over the plans.
Brexit supporters are also anxious the plan will limit British ability to forge trade deals with countries like the United States, and amounts to a "Brexit in name only".
The plan agreed at May´s country retreat at Chequers would involve Britain pursuing a "UK-EU free trade area" for goods that would involve regulatory alignment with the EU.
China says its tariffs on United States goods will take effect immediately after Washington's tariffs on Chinese goods kick in. Mexico is also studying how to reduce the economic strain of an escalating trade spat, an action that China has also adopted.
The products have been available for sale at Woolworths , ALDI and IGA , Campbells and independent grocery stores. Only ALDI products with country of origin Belgium, Hungary or the United Kingdom are affected by the recall.
France players celebrate Samuel Umtiti's goal. "There is still one more step to take, but we are proud of what we have done". One thing to keep an eye on in this match is the legs and how exhausted the players will be, especially with Croatia.
But there was consolation for Fox in claiming one of the remaining slots for the British Open at Carnoustie later this month. The New Zealander had that putt for the title but missed on the high side and the pair were left to go back up the last.
Trump, interjecting, asked why that was - and Stoltenberg responded it was "because of your leadership and your message". Trump is reportedly considering imposing sanctions on the five European countries involved in the pipeline project.
He sank a five-foot birdie putt at the fourth and one twice as long at the fifth before dropping a 32-footer at the sixth. They went back to the 18th tee for the playoff, and Knox pitched from 131 yards to virtually the same spot on the green.
In the video captured by Irizarry, she is heard explaining to the inebriated man that Puerto Rico is "part of the United States". Irizarry is standing in a picnic area, which she tells the officer she has a permit for to attend a birthday party.
Sterling's main role in the side is not to create space for himself, but to create space for the likes of Lingard, Alli and Kane. Beckham and Sir Geoff Hurst, though, defended Sterling's displays after the quarter-final win against Sweden.
Sorenstam won by two shots over Se Ri Pak when she shot her 27 under at Moon Valley at a tournament that no longer exists. Kim, who had a 63 on Thursday and a 65 on Friday, got rolling with an eagle on No. 3 and added six birdies.
He added that OPEC principles would never allow political pressures to change the directions of the market. Now, President Trump is threatening sanctions against any country that continues to do business with Iran.
WH Suspends $10.4B in Obamacare Insurer Payments
Trump tweeted dozens and dozens of times about Obamacare and its demise previous year as he pushed the Senate to repeal the law. The news comes at a critical time for the Covered California exchange, which was set to announce rates for 2019 this month.
Britain to fine Facebook over data breach
Cambridge Analytica used data from millions of Facebook accounts to help Donald Trump's 2016 presidential election campaign. The watchdog also plans to bring criminal charges against Cambridge Analytica's defunct parent company SCL Elections.
Superhero Serena is close to her best, says Bartoli
During his news conference Monday, Federer was asked about potentially playing the final at the same time as the World Cup final. Probably because at the French Open a couple weeks ago I had so much pressure. "I went for it", Serena said. "I just felt calm".