Washington said that Burns would not act as a negotiator and not meet Jalili separately.
He is to put forward the White House position that Iran must give up enrichment for any talks to start.
The US had said previously it would not be involved in any pre-negotiations with Tehran unless it gave up uranium enrichment.
"Bill Burns will reiterate our terms for negotiation remain the same," an official, who asked not to be named, said.
The US presence at the meeting did not indicate a restoration of full diplomatic ties, the official said.
US officials said Washington wanted to take advantage of what appeared to be "debate" within the Iranian government over the nuclear programme.
In addition, Washington believed that three rounds of UN sanctions against Iran, as well as bilateral sanctions by the US and EU nations, were starting to take effect and that it was the time to take advantage of that.
Mahmoud Ahmadinejad, the Iranian president, said on Monday that Jalili and Solana were to discuss a timetable for future negotiations to break the deadlock.
"It is possible that, in the near future, talks in different fields will take place with the United States," he said.
In June, Solana presented Tehran with a package of economic and other incentives proposed by world powers.
Iran has repeatedly refused to suspend its uranium enrichment process - as demanded by the six powers - before formal negotiations can begin on the offer.
Iran, the world's fourth largest oil producer, denies it wants to build nuclear weapons, saying its programme is designed to make electricity to increase its output of oil and natural gas.
There has been opposition within the Bush administration over whether to deal directly with Iran. George Bush, the US president, has made clear all options remain on the table, including military action.
Last week, tensions heightened when Iran test-fired missiles in the Gulf.