Treasury official said on Monday.
The transfer of Iran's oil funds will likely be done by banks that already have Iranian accounts, the official said.
India is Iran's second-largest buyer and owes Tehran about $5.3 billion for oil shipments, according to government and refining sources. Payments by Indian refiners to Iran could resume through Turkey's state-run Halkbank, a route used until February.
The National Iranian Oil Company (NIOC) asked Indian refiners in mid-October to settle some of their payments in euros via Halkbank as soon as possible. Refiners are awaiting the all-clear from the Indian government before transferring any cash.
"Next week if it is possible, we will start making our payments," said P.P. Upadhya, managing director of Mangalore Refinery and Petrochemicals Ltd, one of the Indian buyers of Iranian crude.
A government official also said payments would be expedited once the payment mechanism via Turkey opens up.
"If that Halkbank route opens up ... rather than pushing this to a later date, perhaps this money will go to the Iranians sooner rather than later," said the official, who had direct knowledge of the matter.
The transfer of funds may help the US Treasury Department more closely monitor how Iran plans to use the cash, the US official said.
"One of the things that we spend a lot of time doing is looking at how the Iranians are trying to access this stranded revenue, and heading them off at the pass," the official said.
"And I think the Iranians know if they continue to try to continue to get access to any of this revenue in other fashions (outside the agreement), that that's going to blow up the deal."
Banking and industry sources in South Korea and Japan said they were awaiting details of the weekend agreement before they could decide on how to transfer money to Iran.
South Korea has $5.56 billion stuck in bank accounts, with a similar amount held up in Japan since the beginning of the year, according to sources.
In China, Kunlun Bank, owned by China National Petroleum Corp, holds the Iranian oil dues. Iran has previously said China, its top oil buyer, owes it around $22 billion.
The 1 million bpd ceiling on Iranian exports is sharply below the pre-sanctions level of around 2.5 million bpd and gives Iran very little room to boost sales. Its oil exports in the first nine months of the year have averaged about 1.08 million bpd, according to Reuters data.