The department also said US engagement with Iran would come "if and when" President George W. Bush determines the time is ripe.
Analysts had thought US aid to earthquake victims in Bam, southern Iran might open a door to rapprochement, but US officials said Iran is still developing nuclear weapons and hampering democracy.
"Our policy has been to engage Iran on specific issues of concern in an appropriate manner if and when the president determines he wants to do so," State Department spokesman Richard Boucher said.
"I don't want to speculate at this point of whether there might be such discussions again but we do think these issues need to be addressed," Boucher told reporters.
Boucher said Washington continues to have "issues with Iran."
"Issues like the voices of people in Iran that look for more freedom, issues like al-Qaeda members who are in Iran, issues like Iran's nuclear program, which needs to be resolved in a satisfactory manner consistent with Iran's promises and commitments to the international community," Boucher said.
He said the two countries had broached some of these issues, alluding to secretive US-Iranian diplomatic talks in Geneva last May.
However, Iran's former president said Friday that it was time for the United States to put such "accusations" behind it.
The Islamic republic's former president Ali Akbar Hashemi Rafsanjani said the United States must stop making accusations against Iran if it wants to open a new page in relations with Tehran.
"If the United States wants to extend the hand of friendship and turn a new page, they should stop repeating past accusations (against Iran) which are totally false," Rafsanjani said at weekly Friday prayers in the Iranian capital.
The two countries broke off relations in 1980 following the Islamic revolution that deposed the Shah of Iran. Bush has described Iran as part of the "axis of evil."
Iran's supreme leader, Ayatollah Ali Khameini, said Thursday that US humanitarian aid for the victims of the Bam earthquake had not improved relations, saying Washington continues to show "basic hostility" toward Iran.
In Washington, US Secretary of State Colin Powell, on Thursday, seemed more upbeat on diplomatic prospects following the dispatch of US aid to the quake zone.
"This is not a political breakthrough, but it was nevertheless a human breakthrough ... so we will see what happens in the future with respect to our relationship with Iran," Powell said.