It is hoped the meetings can revive faltering negotiations on an agreement that will provide a comprehensive solution to the Iranian nuclear issue.
Iran's lead negotiator said he was optimistic consensus could be reached before the 20 July deadline for a deal.
Differences reportedly remain over how much uranium enrichment capacity Iran should be allowed to keep.
Both sides are hoping to build on an interim deal agreed in Geneva in November that saw Iran curb enrichment in return for sanctions relief.
The so-called P5+1 - the US, UK, France, China and Russia plus Germany - want its sensitive nuclear activities scaled back permanently to ensure that it cannot assemble a nuclear weapon.
But Iran says its nuclear work, which it insists is peaceful, will continue - and wants an end to the sanctions that have crippled its economy.
The US government believes the negotiations on a long-term deal have reached a "critical moment" and has sent two of its most senior diplomats to Geneva - Deputy Secretary of State William Burns and Jake Sullivan, a top White House adviser.
Iranian Deputy Foreign Minister Abbas Araqchi said he was optimistic about meeting next month's deadline.
"If this does not happen, we'll have to resort to extending the Geneva agreement for another six months so the negotiations can continue," the state news agency Irna quoted him as saying.
A senior US official said the talks would give both sides "a timely opportunity to exchange views" before the next full round of negotiations between Iran and the P5+1 in Vienna next week. The last round in May reportedly made little progress.
The BBC's Imogen Foulkes in Geneva says big differences remain over how much, if any, uranium enrichment capability Iran should be allowed.
Tehran is keen to have the sanctions that have crippled its economy lifted, but says it does not want to rely on foreign suppliers of enriched uranium for its nuclear reactors.
Washington meanwhile will not lift sanctions if it suspects Iran is enriching uranium to make nuclear weapons.
But, our correspondent adds, the fact that both sides are travelling to Geneva is an indication they remain keen to reach an agreement.
Senior US and Iranian officials have begun two days of direct talks in Geneva on Iran's nuclear programme.