“I personally intend to visit as soon as the situation here allows,” Mr. Dostum said in the interview, which was conducted and broadcast in Dari.

He assured listeners that he had many friends in Washington — “I am well acquainted with our Pentagon friends and congressmen,” he said — and that he would tell them how things were in Afghanistan.

“I want to discuss the situation with them,” he said. “They have to take this issue seriously. Otherwise, it might get out of control.”

That discussion seems unlikely to happen anytime soon. Mr. Dostum’s inability to secure entry to the United States is in fact a longstanding issue.

In 2013, Representative Dana Rohrabacher, a California Republican who has known Mr. Dostum for decades, personally asked Secretary of State John Kerry to grant him a visa. At the time, Mr. Rohrabacher said he was seeking to bring Mr. Dostum to Washington to discuss the war and the future of the Afghan government.

No visa was issued then, and Mr. Dostum’s election as vice president the following year has not changed the Obama administration’s view of him or its willingness to let him visit the United States, said two senior American officials, who spoke on the condition of anonymity to avoid antagonizing the Afghan government. American officials do not want to be seen with him, one said.

At the outset of the war, Mr. Dostum fought alongside Central Intelligence Agency operatives and Special Operations forces to oust the Taliban, and he was initially very close to the United States military. In the years immediately after the Taliban fell, he was known to show American guests at his compound in the northern city of Shibarghan a pistol that he said had been given to him by Gen. Tommy R. Franks, who was then in charge of the United States Central Command.