"The PM said that the draft text put forward by the European Commission yesterday was unacceptable to the UK as it would, if implemented, undermine the UK common market and constitutional integrity of the UK," the press release read.
According to the press release, May stressed that she, as well as Irish Prime Minister Leo Varadkar, saw the resolution of the border issue as a priority.
The prime minister also reiterated London’s commitment to "turning the Joint Report agreed in December into legal text as soon as possible," the press release added.
The press service noted that May had briefed Tusk on her upcoming speech on the UK's vision of future economic partnership with the European Union and expressed hope that European leaders would engage with UK initiatives constructively.
The border between the Republic of Ireland and Northern Ireland remains an obstacle on the agenda of the Brexit talks, as London's pullout might create difficulties for the free movement of goods and workers between Ireland and the Northern Irish counties of the United Kingdom and return a "hard" border between them in potential violation of the 1998 Good Friday Agreement.
On June 23, 2016, the United Kingdom voted in a referendum to leave the European Union. The negotiations between the United Kingdom and Brussels are due to be completed by the end of March 2019.