The European Union and Britain, which are hurtling toward a costly, damaging no-deal split in a little over two months, started a high-wire week of diplomacy Tuesday by entrenching themselves deeper in their irreconcilable positions.

Highlighting Prime Minister Boris Johnson’s determination to leave the bloc on Oct. 31 even if no divorce deal is in place, his government said as of Sept. 1 it would stop attending all European Union meetings where its vital interests were not at stake. Mr. Johnson’s office at Downing Street doubled down on the message later, stating that unless the trade backstop on the Irish border was abolished, “there’s no prospect of a deal.”

The European Union, which is not known for its speedy diplomacy, took only half a day to rebuff a four-page proposal by Mr. Johnson on breaking a deadlock over ensuring a transparent border between Ireland, a member of the bloc, and Northern Ireland, which is part of Britain. The bloc said that one key part of the proposal was “incorrect” and another was “misleading.”

In the diplomatic note from the European Commission and Council to the bloc’s remaining 27 nations, which was obtained by The Associated Press, the member states were strongly urged not to give in to Johnson’s demand that the legal withdrawal agreement the European Union negotiated with his predecessor, Theresa May, be changed at this late stage.