The DUP has held talks with Prime Minister Boris Johnson at Downing Street.
Arlene Foster and Nigel Dodds emerged from No 10 on Tuesday afternoon saying it had been a “very good meeting”.
In a statement, the party leader said Boris Johnson rejected the idea of a Northern Ireland-only backstop.
“The Prime Minister rejected a Northern Ireland only backstop in a letter to Donald Tusk on 19 August,” said Arlene Foster.
“It is undemocratic and unconstitutional and would place a tariff border between Northern Ireland and the rest of the United Kingdom.
“That would be unacceptable.
“During today’s meeting, the Prime Minister confirmed his rejection of the Northern Ireland only backstop and his commitment to securing a deal which works for the entire United Kingdom as well as our neighbours in the Republic of Ireland.”