"Today's meeting might continue with several others so that the viewpoints of all sides can be put on the table so that we reach ... agreement," he told reporters.
He did not elaborate what he meant by agreement, but added that he hoped the talks would pave the way for agreeing on "a modality and a framework" for further negotiations.
Iran's chief nuclear negotiator Saeed Jalili also spoke of his "positive intentions" as he arrived in Geneva on Friday for the talks with officials from the United States, Russia, China, France, Britain and Germany - the so-called sextet.
Neither Jalili, Burns nor EU foreign policy chief Javier Solana spoke to reporters as they went into the first session of talks on Saturday.
Iran, the world's fourth-largest oil producer, rejects suspicions that it wants the atom bomb, saying the aim of the nuclear programme is to generate electricity so that it can export more oil and gas.
Western diplomats say they want the talks to clarify Iran's response to an offer, delivered last month, of technical and commercial incentives to suspend uranium enrichment.
Asked about the Iranian officials' rejection of suspension, Solana's spokeswoman Cristina Gallach said: "We have to wait to this afternoon to see the Iranian position. We are ready to look at creative manners to allow negotiations to start in full agreement with the U.N. Security Council."
The U.N. has imposed three sets of sanctions on Iran in a stand-off that goes back to the revelation in 2002 by an exiled opposition group of the existence of a uranium enrichment facility and heavy water plant in the country.
Tension has intensified since Tehran tested missiles last week, alarming Israel and unsettling energy markets on fears that conflict could disrupt supply.
Yet oil prices slipped on Friday, ending 13 percent down from last week's record of over $147 a barrel of crude.
Traders cited as factors the attendance of Burns - a career diplomat who helped restore U.S. ties with Libya in 2006 - and a comment by Mottaki that the chances of an Israeli or U.S. strike were "almost zero".
