LONDON — Faced with a growing backlash over his decision to suspend Parliament next month, Prime Minister Boris Johnson on Thursday sought to calm the furious reaction by promising to accelerate efforts to reach a new Brexit agreement with Brussels.

His statement came after another day of Brexit turbulence, two resignations from within his own party, and claims from critics that the government was trampling the conventions of the country’s unwritten Constitution, undermining its democracy.

[What did Boris Johnson just do to Parliament? An explainer.]

Mr. Johnson’s move to suspend Parliament in September makes it significantly harder for lawmakers to pass legislation preventing Britain from leaving the European Union without an agreement — a step his critics were planning.

But in his latest swerve, Mr. Johnson promised that Britain’s Brexit negotiators would sit down with their European counterparts twice a week through September, with the possibility of additional technical meetings, to try to reach a deal that would avert the risk of a cliff-edge departure.