As Jalili arrived, he was aware that the expected presence of Burns at the weekend meeting had raised the political stakes.
This is the highest-level public engagement between Tehran and Washington since Iran's Islamic revolution three decades ago, and both sides have welcomed it with guarded optimism.
Major policy shift
The decision to send Burns is being seen as a major policy shift on the part of the US.
Ann Somerset, a state department spokesperson, told Al Jazeera on Friday that "this is not a negotiation".
Burns has been sent to Geneva "to underscore our commitment to a diplomatic solution to the issue ... but we are not there to negotiate", she said.
However, Condoleezza Rice, the US secretary of state, acknowledged that the US had shifted its position on diplomacy with Iran, but insisted that Tehran must suspend its enrichment and reprocessing of nuclear materials for substantive talks with Washington.
|Iranian officials have welcomed Burns' participation at talks in Geneva [EPA]
"The United States doesn't have any permanent enemies," she said in Washington on Friday.
"We have been very clear that any country can change course."
Iranian experts say agreement could come down to a sophisticated understanding of that process.
Al Jazeera's Richard Bestic said success would have benefits for both sides.
Iran is the world's largest producer of oil, and any resolution of the nuclear crisis could ease the problems caused by high global oil prices.
For Iran, unemployment and inflation are a double-headed dilemma that would be helped by reduced global tensions, strained by the missile tests it carried out last week.
But what is not clear is how Jalili will respond to what is being offered in return for a freeze on Iran's nuclear ambitions.
Before his departure from Tehran airport, Jalili underscored the importance of attitudes.
"What matters to us is the approach the other side takes. More important than who is going to participate is the kind of approach they take," he said.
"If it is constructive, we could have positive talks".
Jalili's positive words were reciprocated by Rice.
"This decision to send Undersecretary [Burns] is an affirmation of the policy that we have been pursuing with our European allies ... for some time now," she said.
"It is, in fact, a strong signal to the entire world that we have been very serious about this diplomacy and we will remain very serious about this diplomacy."
Rice pointed out she had endorsed the proposal from the so-called P5 plus one - the US, France, Britain, China, Russia and Germany - on incentives to advance talks with Iran on halting its nuclear programme.
She described sending Burns to Geneva to meet Jalili and Solana as the "book end" to that move.
Earlier on Friday, Iran's foreign minister said his country is prepared to have dialogue with the US on establishing a US interests section in Iran and beginning direct flights between the two countries.
Manouchehr Mottaki said during a visit to Turkey that Tehran was aware of media reports saying Washington was interested in opening the diplomatic office.
"In my opinion, talks and a deal on an American bureau in Iran and direct flights between Iran and the United States is possible," he said after holding talks with Ali Babacan, his Turkish counterpart, in Ankara.
If such a bureau were to be opened, it would mark the first such link between the two countries since the Islamic Revolution in Iran in 1979.
The US already has a similar office in Cuba.