Washington has said it won't issue a visa to newly appointed Hamid Aboutalebi, who has been linked to the 1979 US hostage crisis.
Iran, in response, has insisted the objection is unacceptable and threatens to cloud a gradual thaw in relations between the two enemies after decades of mistrust.
The spat comes as Tehran and world powers engage in negotiations aimed at transforming a temporary accord on Iran's nuclear program into a permanent agreement.
"Nothing in this quite public confrontation so far has had any impact on that," Ambassador Samantha Power said.
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"Again, so far we had talks just last week. We'll have more high level talks in the next month," she added when prodded about potential harm.
"And our experts are meeting every day. We have not seen this issue influence those talks in any way. And the urgency, of course, of that issue is plain to everyone."
Now the powers want Iran to reduce permanently, or at least long-term, the scope of its program in order to make any dash to create an atomic bomb extremely difficult and easily detectable.
Iran in return wants all sanctions lifted.
"We would expect that Iran's own interest in getting out from under economic sanctions, which is what it says it wants -- our interests, certainly, in making sure that Iran doesn't possess or develop a nuclear weapon, that that's what is going to be paramount here," Power said.
As the host government, the United States is obliged to issue visas to diplomats who serve at the United Nations, headquartered in New York.