by Larry Neild

LONDON, Sept. 21 (Xinhua) -- British Prime Minister Theresa May gave her first full reaction Friday following a two-day bruising meeting with EU leaders in the Austrian city of Salzburg, making it clear that she rejected any Brussels proposals that would mean a border to keep Northern Ireland as part of EU rules and regulations.

In a seven-minute speech in Downing Street, May said she rejected a proposal by the EU for Britain to be part of an EEA area that would tie Britain to all EU rules, including free movement of people.

In a stark warning to Brussels, May said: "The EU should be clear, I will not overturn the result of the referendum nor will I break up my country. We need serious engagement in resolving the two big problems in the negotiations and we stand ready."

The June 2016 referendum, she said, was the biggest democratic exercise in British history.

Media in London reacted to the meeting in Austria, describing the way May had been treated as an ambush.

In what was seen as the way she had been treated in Salzburg, May said she and British negotiators had always acted with "nothing but respect" and she expected the same from Brussels.

May said it was now up to the EU to explain why they were rejecting her proposals and it was now up to them to put forward their proposals.

She also gave an assurance to the 3 million EU citizens living in Britain that even if there was no deal, their rights to stay would be assured.

At the heart of the wrangle is the so-called Chequers Plan, May's blueprint for Britain's future relationship with the EU after next March.

Her plan was drawn up at a meeting of her ministers in the summer at her country retreat, Chequers.

The Salzburg meeting ended with European Council President Donald Tusk saying that although there were some positive elements in May's proposals, the framework she suggested for economic co-operation will not work as it undermined the European single market.