KABUL, Afghanistan — The State Department said it was cutting $1 billion in aid to Afghanistan this year, and potentially another $1 billion in 2021, after Secretary of State Mike Pompeo failed to persuade rival Afghan leaders in a meeting on Monday in Kabul to support a unified government, which American diplomats consider crucial to preventing peace negotiations from falling apart.

Mr. Pompeo’s announcement came as he was flying back to the United States after meeting with President Ashraf Ghani and the Afghan former chief executive, Abdullah Abdullah, in an attempt to mediate between the two rivals who both claim to be the legitimate president — a crisis that threatens to split the government apart and sink hopes of ending the war.

For the top American diplomat to travel halfway around the world in the middle of the global coronavirus epidemic signaled how seriously the United States was taking the internal Afghan bickering and the risks posed for both countries. And the cutoff in aid, a major blow to the Afghan government, revealed just how frustrated the United States was with the impasse, which further imperils an already precarious peace deal.

“The United States is disappointed in them and what their conduct means for Afghanistan and our shared interests,” Mr. Pompeo said in a statement. “Their failure has harmed U.S.-Afghan relations and, sadly, dishonors those Afghan, Americans and coalition partners who have sacrificed their lives and treasure in the struggle to build a new future for this country.”