She said a meeting involving "all the stakeholders and interested parties" should take place by the end of the month.
"If we move forward with such a meeting, it is expected that Iran would be invited as a neighbour of Afghanistan," Clinton said in Brussels on Thursday.
The Iranian spokesman emphasised his country's interest in the conference was "to help Afghanistan".
"For us, Afghanistan is very important. Afghanistan's security is our security, Afghanistan's progress is our progress and Afghanistan's stability is ours," Elham said.
"Our issue is Afghanistan - our issue is not them [the US], our issue is not Nato," he said.
Alireza Ronaghi, Al Jazeera's Tehran correspondent, said this was the first time that such an invitation has been mentioned by a high-ranking US official.
"Of course there has been some level of talks between Iran and America about Iraq in Baghdad, but this one, if it takes place, is going to be something unique," he said.
Clinton's mention of including Iran in talks on Afghanistan represents a sharp turnaround from the previous US administration.
Barack Obama, the US president, has said he wants to talk to Iran on a range of issues and the conference invitation would be the start of a diplomatic outreach to Tehran.
The United States is said to be carrying out a review of their isolationist policies towards Iran, including whether to open a low-level diplomatic office in Tehran.
However, Washington remains at odds with Tehran, primarily over its nuclear programme, which Washington says is aimed at building an atomic bomb.
Tehran says its programme is for peaceful power purposes.
The United States cut off diplomatic ties with Tehran during the 1979-1981 US hostage crisis, in which a group of Iranian students held 52 US diplomats hostage at the American embassy for 444 days.