Relations between Iran and the United States continue to be marked by deep "mistrust," a State Department spokeswoman said Monday, as thousands in Tehran took part in anti-American protests.

The demonstrations marked the day in 1979 that Islamist students stormed the US embassy compound in the Iranian capital, holding 52 American diplomats hostage for 444 days.

The standoff led to the severing of diplomatic ties and decades of tense relations, though a recent breakthrough saw President Barack Obama and his Iranian counterpart Hassan Rouhani hold a telephone call in September.

State Department deputy spokeswoman Marie Harf, however, said the huge turnout in Tehran on Monday, including chants of "Death to America!", showed the depth of longstanding problems between the two countries.

"We've all been clear that this is tough, and that there's a deep history of mistrust here. I think you saw that today with some of the protests we saw in Iran," she said in Washington.

Harf said the United States remains wary of Iran's suspect nuclear program, a longstanding obstacle to improved ties, amid international efforts for a negotiated solution.

"We are squarely focused on stopping the advance of Iran's nuclear program, gaining more transparency into their nuclear activities and negotiating a long-term comprehensive solution to this issue," she said.

"Obviously it's not easy, but we have an opportunity here and an obligation to see where this diplomatic path might lead because it's all of our preference just be resolved diplomatically."