The senior U.S. official in Geneva said Zarif's "thoughtful presentation" in New York leads Washington to expect "something substantial" from the Iranian delegation at this week's talks.
But the official said the United States is "clear-eyed about what is very, very difficult work" and what is likely to prove a bumpy road full of hurdles.
"No one is naive," the official said.
In February, the group known as the P5 plus one offered Iran a package of economic incentives to abandon its nuclear ambitions.
In exchange for easing sanctions barring trade with Iran in gold and other precious metals and petrochemicals, the group wants Tehran to shut its underground enrichment facility at Fordo, near the holy city of Qom.
The group also wants Iran to ship its stockpile of uranium enriched to 20% purity, seen as a jumping part to producing weapons-grade uranium.
Iran wants the international community to acknowledge its right to enrich uranium under the Non-Proliferation Treaty.
The six negotiating countries group has balked at that, although privately some diplomats say a final deal could allow Iran to enrich uranium to a low purity, such as 3% - 5%.
They also proposed fuel for a medical reactor and easing sanctions on aviation spare parts as part of the deal.
The international community has expressed suspicions over enrichment, fearing Iran may secretly be transforming nuclear fuel into atomic bomb-grade materials.
Iran has never formally responded to the deal. It remains to be seen whether the group would ultimately be willing to sweeten the offer in the new climate, although U.S. officials said no new offer will be made to Iran at this week's talks.
Robert Einhorn, one of the U.S. negotiators with Iran until he left the State Department in May, said Iran's new negotiating team is motivated to negotiate more seriously than the previous team.
"This group really wants to reach a deal," said Einhorn, now at the Brookings Institution. "I don't know if our minimum requirements will overlap with their minimum requirements, but they are realistic enough to know sanctions won't be eased and eventually lifted without some curbs on its nuclear program.
Rouhani and Zarif appear to have the backing of Iran's Supreme Leader, Ayatollah Ali Khamenei, who has said he supports "heroic flexibility" in negotiations to ease sanctions.
But their room to maneuver may be limited.
Einhorn said the Iranians will need to show results fairly quickly to keep Khamenei's backing.
"The Supreme Leader has basically given them some running room," he said. "He's skeptical it will achieve anything, but has said they can go ahead and try this moderate approach and see where it gets them. But their mandate is not infinite. I don't know if there is a time limit but they genuinely need to show this moderate approach can work."