"If there is no agreement on a deal that is acceptable to the United Kingdom, then we're preparing for no deal", she said at the news conference after the summit in Austria.
However Mrs May has rejected the plan as unacceptable arguing that it would effectively create a border in the Irish Sea between Northern Ireland and the rest of the UK.
"Concerns have been raised and I want to know what those concerns are", she said.
Maintaining a united front that refuses to let May bypass the talks run by European Union negotiator Michel Barnier, the 27 leaders did not respond to her.
During a speech in Salzburg, where May met with European Union leaders over dinner last night, he said that no Brexit agreement can be reached without a solution to the Irish border issues, and "while there are positive elements in the Chequers proposal, its suggested framework for economic cooperation will not work, not least because it risks undermining the single market".
"The Brexit teaches us something - and I completely respect British sovereignty when I say that - it showed that those who say that we can easily live without Europe, that everything is going to be alright, and that it's going to bring in a lot of money are liars", he said.
- Dutch Prime Minister Mark Rutte said his country is better prepared for a no-deal Brexit than Britain and an agreement is "not easy" because of Mrs May's red lines.
Officials on both sides of the Channel hope this summit will give new impetus to divorce negotiations ahead of a crunch summit in Brussels on October 18.
The bloc also raised the stakes by putting on ice a special summit planned for November to seal a deal, saying it would only happen if there is progress next month. "And at various stages of these negotiations, tactics would be used as part of those negotiations".
This would keep Northern Ireland under EU economic oversight if London and Brussels can not agree a trade pact to keep UK-EU borders open after a transition period ends in 2020 - an idea that Mrs May and a small party in the province that props up her minority government oppose.
However, May repeated her warning that Britain would never agree to any "legal separation of the United Kingdom into two customs territories".
"Our White Paper remains the only serious and credible proposition on the table for achieving that objective".
The Prime Minister has said that she intends to "take back control" over the country's borders and laws which aligns with a hard Brexit.
"The UK will leave on March 29 next year", she said over dinner, adding: "The onus is now on all of us to get this deal done".
Two days later, she has been sent away from Austria with a similarly blunt response: change the Chequers plan or it's no-deal.
But "unfortunately we can not at this stage exclude a no-deal - it depends on both sides of negotiations".
Theresa May, however, speaking outside the informal summit, said a Conservative government would not permit a second referendum on Brexit.
He said May had irked European Union leaders with an uncompromising article Wednesday for German newspaper Die Welt, followed up by a similar summit dinner speech and an unproductive sideline meeting with Irish Prime Minister Leo Varadkar.
Tusk and Macron had torn into May's so-called Chequers plan, which they believe will fragment the bloc's prized single market and "not work".
May told reporters that her offer to solve the border riddle - the biggest obstacle to a deal - was "the only credible and negotiable plan on the table that delivers no hard border in Northern Ireland and also delivers on the vote of the British people" to leave the EU.
"With just weeks to go until a deal must be struck, the Prime Minister can not keep ignoring this reality".
Most EU leaders "would welcome a situation where there is the possibility of the British people putting things into perspective, seeing what has been negotiated, seeing the options, and then deciding once and for all", he added.
Sheffield saw almost half a month's rain fall in 24 hours, while more than half a month's rain fell in Sennybridge in Wales. What's more the gusts are likely to leave a lot of debris around, which could potentially cause problems for commuters.
What we thought was Apple-specific visual design has been carried over to Google's navigation app, right down to the typeface. Unlike Apple Maps, it is not now possible to use Siri to enter destinations and otherwise control Google Maps .
Chinese firms with factories in the United States would also face higher costs as they ship USA -assembled products back home. He announced last week that he will step down within a year and hand the company reins to chief executive Daniel Zhang.
He had a reputation as a tough leader who was influential within the inner circles of the country's communist party. Some 97 activists have been jailed as of April this year, according to Amnesty International.
Before the rally, Trump told Hannity that he thinks "it's a sad situation" and said that Kavanaugh is an "outstanding person". Ford's lawyers said on Tuesday she would testify before the committee only if the FBI first investigated her allegation.
However, its dominance is threatened by Aldi and Lidl, which combined enjoy a 13.1 per cent share of the grocery market. The offer is similar to the Lidl Pick of the Week and Aldi Super Six offers, which change on a weekly basis.
Pixel size has increased, which should bring better low-light performance and help the "Smart HDR" feature, according to iFixit . Its 4.7-inch screen is adequate and on par with other smartphones, even though its resolution falls short of high definition.
At the same time, Florence's drenching rain - as much as 3 feet in some areas - left many areas near the coast underwater. There is no timetable for the road to be reopened. "This is going to be a lot worse", Fraboni told CNN affiliate WBTW .
The most notable mechanical revision to the vehicle has been a 140mm raise in ride height, allowing better off-road ability. While it is a concept, the futuristic looking truck still looks similar to the production model Navara .
Tour Championship preview: DeChambeau, Rose favorites
The Tour also announced an attempt to put more spice in the regular season by launching the $10 million "Wyndham Rewards Top 10". The course in Maryland has hosted four major tournaments, the U.S Open on three occasions and the US PGA Championship once.
Maria-hit Puerto Rico passes one-year mark
For months, the US government contended that the official death toll from the hurricane and the three months afterward was 64. While the US government has invested billions of dollars to help clean up and fix the USA territory, much work remains.
Elite Iranian soldiers killed in attack on military parade
Semi-official news agency Mehr said further shooting broke out as some of the attackers who managed to escape were being chased. Zarif on Twitter warned that "Iran will respond swiftly and decisively in defence of Iranian lives" after the attack in Ahvaz.
Mass Flu Shot Clinic Scheduled October 4
That's why the CDC is urging people to act now, just before the October start of the 2018-19 flu season and get vaccinated. Vaccines are specifically created to protect you from the flu without exposing you to a virus that will make you sick.
Liverpool 3-2 Paris Saint-Germain
Neymar should not be blamed for Paris Saint-Germain's 3-2 Champions League loss at Liverpool , according to skipper Thiago Silva. Then Mbappe stunned the raucous Anfield crowd with a clinical finish only to see Firmino grab the glory.
Emery warns Arsenal against leaking late goals
I will work hard every day to play more games. "I came to the club to play every game", Leno said . "We have fun together". Vorskla coach Vasyl Sachko conceded his team were second-best but is hopeful they took some lessons from the game.