To underscore the point, the White House also took the unusual step of making that assurance public in a news release that was issued the day before Mr. Barzani arrived for talks here this week with Mr. Biden, President Obama and other senior officials and lawmakers.

Mr. Barzani, concluding his nearly weeklong visit, said that his main concern had been to ensure that weapons got into the hands of Kurdish pesh merga fighters as quickly as possible, and that the White House had assured him that they would receive “the necessary weapons.” But even as Mr. Barzani made clear that he was not openly challenging White House policy, he did not back away from his desire for direct assistance.

“The problem between the Congress and the White House is something that we will not interfere with,” Mr. Barzani told reporters, speaking through an interpreter. “But if we are asked, we would prefer these weapons to be sent to us directly.”

Mr. Barzani did not repeat earlier appeals by Kurdish officials for heavy weapons like tanks and helicopters, systems that would aggravate the Iraqi government’s concerns, and that American officials have said would take years to provide if the United States were ever prepared to deliver them. Instead, he said that the United States should provide weapons that Kurdish fighters were familiar with or that would require “short-term training.”

In an appearance at the Atlantic Council this week, Mr. Barzani suggested that the Kurds had deferred, but not abandoned, their dream of independence. He said that a referendum on independence would be delayed until the fight against ISIS was over, and that the unity of Iraq was “voluntary and not compulsory.”