"The door is open for negotiations, let's see if together we can go through."
Solana said talks with Larijani would seek to "prepare a route that leads to a negotiated solution to this conflict".
Solana issued a statement on Saturday night, immediately after the UN resolution was passed in New York, that confirmed the continued "twin track" approach by the Europeans, US and other world powers.
That involves gradually imposing tougher sanctions if Iran fails to halt uranium enrichment but offering negotiations on economic and political advantages for Iran if it falls into line.
"We want to be as generous as possible," Solana said.
Solana led largely unsuccessful international diplomatic efforts for months to persuade Iran to stop uranium enrichment before the UN first decided to impose sanctions in December.
He last met with Larijani at a security conference last month in Munich, and the two have spoken once on the telephone since then.
"If we halt our nuclear programme it will cost us more than any sanctions"
Hesam, Tehran, Iran
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Frank-Walter Steinmeier, Germany's foreign minister, also urged Iran to comply with UN resolutions "in order to clear the way for the start of negotiations".
The sanctions, approved unanimously by the Security Council, include banning Iranian arms exports and freezing the assets of 28 people and organisations involved in Iran's nuclear and missile programmes.
Iran says its nuclear programme is aimed at peaceful uses such as producing electricity, but the US and Europeans fear it could be used to make nuclear weapons.
International pressure is mounting on Tehran to free the 15, who were seized in the Shatt al-Arab waterway between Iran and Iraq on Friday as they conducted "routine" anti-smuggling operations.
Solana reiterated the EU's concern about the fate of the sailors and marines. He insisted the crisis over the seizure of the seamen should not be linked to the nuclear issue.
"I don't think that this should be mixed, one thing with the other," he said, reflecting European concerns that Iran might take a tougher line on the captured Britons if the sanctions were adopted.
Meanwhile, Britain's ambassador to Tehran, on Sunday, asked to see the soldiers and demanded that they be released.
Geoffrey Adams met foreign ministry officials after his return to Iran, a British diplomat told AFP.
"He asked them for information about where the 15 British sailors are being detained and the possibility of meeting them," he said.
"He also demanded their immediate release."
However, the Iranian officials did not say where the Britons were, the diplomat said.
Iran said on Saturday that the 15 had admitted to violating its territorial waters.
Also on Sunday, Israel said it welcomed the UN Security Council decision to put new sanctions on Iran.
"There is no doubt that this resolution is a step up in international efforts to stop Iran's nuclear programme," Ehud Olmert, Israel's prime minister, said.
"We can already say that the previous resolutions ... have considerably influenced not only the international community's approach, but also Iran's conduct."
Israel, widely considered the Middle East's sole if undeclared nuclear power, considers Iran its number one enemy following repeated calls by Mahmoud Ahmadinejad, Iran's president, for Israel to be wiped off the map.