BRUSSELS -- Talks with British Prime Minister Theresa May were constructive and robust, but the European Union (EU) will not reopen negotiations on the Brexit deal, European Commission President Jean-Claude Juncker said Thursday in a joint statement.

Juncker underlined that the Withdrawal Agreement represents a carefully balanced compromise between the EU and Britain, in which both sides have made significant concessions to arrive at a deal, said the statement read out by European Commission chief spokesperson Margaritis Schinas.

"President Juncker however expressed his openness to add wording to the Political Declaration agreed by the EU27 and the UK in order to be more ambitious in terms of content and speed when it comes to the future relationship between the European Union and the UK," said the statement.

He also drew attention to the fact that any solution would have to be agreed by the European Parliament and the EU27, said the statement.

May arrived in Brussels earlier Thursday to meet Juncker, European Council President Donald Tusk and President of the European Parliament Antonio Tajani for further talks on Brexit concessions despite the EU's repeated denial of renegotiation.

May reportedly aimed to formally ask the EU to reopen the Withdrawal Agreement following the passing by the British Parliament last week of the so-called Brady amendment, which calls for "alternative arrangements" to replace the contentious Irish backstop, the prime minister's spokesman said Tuesday in London.

"Following the vote, work has been taking place on all of the options and it is important for that to take place before we go to Brussels," the spokesman said.