For the Islamic republic, the goal is to make a leap towards ending the international sanctions that have battered its economy.
For Washington and its allies, the aim is to make certain that what Iran says is a peaceful atomic power programme is not a covert attempt to build a nuclear bomb.
The talks, at an upscale Geneva hotel, were expected to last two days.
It is a traditional venue for closed-door diplomatic negotiations, most recently hosting sessions on Syria and Ukraine.
The Geneva meeting marks the first time since the 1980s that Tehran and Washington have held official, direct talks on the nuclear issue outside the wider P5+1 process.
The P5+1 group of permanent members of the Security Council -- Britain, China, France, Russia and the United States -- plus Germany have long sought to reach a settlement over Iran's nuclear programme.
But with the last round of talks in Vienna in May yielding little, there has been concern that the process is stalling.
"We have always had bilateral discussions with the United States in the margin of the P5+1 group, but since the talks have entered a serious phase, we want to have separate consultations," Araqchi said, quoted by official IRNA news agency.
"Most of the sanctions were imposed by the US, and other countries from the P5+1 group were not involved," he added.
The US team in Geneva was to be led by Deputy Secretary of State Bill Burns and Jake Sullivan, a top White House adviser.