America has said it is prepared to open limited talks with Iran but is against restoring normal diplomatic relations at this stage.
Armitage said Iran had shown some co-operation over Iraq
Contacts with the Islamic Republic could be made on issues such as Iraq and drugs, Deputy Secretary of State Richard Armitage told Congress.
The move came after Iran moved to allay fears it is building a nuclear bomb.
Low-level talks broke off earlier this year after the US accused Iran of harbouring al-Qaeda members.
"We are prepared to engage in limited discussions with the Government of Iran about areas of mutual interest, as appropriate," Mr Armitage told the Senate Foreign Relations Committee in Washington.
"We have not entered into any broad dialogue with the aim of normalising relations."
He suggested the talks would not be one-on-one to start with but rather be in some kind of multilateral forum such as the United Nations.
The BBC's state department correspondent, Jon Leyne, says policy towards Iran is fiercely fought over in Washington and Mr Armitage's announcement may not be the end of the matter.
No Iranian reaction to Tuesday's announcement was immediately forthcoming.
Mr Armitage said Iran was withholding information about suspected members of al-Qaeda - the Islamic group held responsible for the 11 September 2001 attacks on America - on its territory.
"Despite public statements that they would co-operate with other countries, the Iranians have refused repeated requests to turn over or share intelligence about all al-Qaeda members and leaders they claim to have in custody..." he said.
"Resolution of this issue would be an important step in US-Iranian relations and
we cannot move forward without this step."
Iran announced on Sunday that it had given the names of extradited al-Qaeda suspects to the UN Security Council but gave no details of detainees still in its custody.
Washington dismissed the announcement, insisting that all al-Qaeda suspects should be extradited to either the US, their
country of origin or third countries.
Iran, however, said that the suspects had committed offences in Iran and would be tried in its courts.
Relations between the two countries have further been strained by suspicions that Iran is seeking to develop nuclear weapons.
Tehran agreed this month to enhanced UN inspections and said it would suspend its enrichment of uranium which could be used to make nuclear weapons.
Warning on Iraq
In another development on Tuesday, US President George W Bush warned Iran - along with Syria - not to let militants cross into Iraq from their territory.
"We are working closely with those countries to let them know we expect them to enforce borders," he said.
In his report to Congress, Mr Armitage noted that there had been some progress in ties with Iran.
Tehran, he said, had made pledges for the reconstruction of Iraq at the Madrid donors' conference and Iran had also agreed to move back some border posts that were on Iraqi territory.