KABUL—The United States started evacuating its diplomats and was sending more troops to help secure Kabul airport and the embassy after the Taliban’s lightning advances brought the Islamist group to the door of the capital in a matter of days. Just last week, a U.S. intelligence estimate said Kabul could hold out for at least three months. “We have a small batch of people leaving now as we speak, a majority of the staff are ready to leave,” a U.S. official told Reuters on Sunday. “The embassy continues to function.” The fall of Jalalabad has also given the Taliban control of a road leading to the Pakistan city of Peshawar, one of the main highways into landlocked Afghanistan. It followed the Taliban’s seizure of the northern city of Mazar-i-Sharif late on Saturday, also with little fighting. “There are no clashes taking place right now in Jalalabad because the governor has …