WASHINGTON, Aug 24 (Reuters) US President Donald Trump and Senate Republican leader Mitch McConnell remain united on many priorities and will hold previously scheduled meetings after the August recess to discuss the issues with members of the congressional leadership and the Cabinet, the White House said on Wednesday. Trump and McConnell "remain united on many shared priorities, including middle class tax relief, strengthening the military, constructing a southern border wall, and other important issues," the White House said in a statement. Earlier on Wednesday, McConnell said he and his team were in "regular contact" with Trump and committed to working together, following weeks of tensions between the two Republicans. REUTERS AKC0412