The US delegation, led by Vice President JD Vance and including President Donald Trump's special envoy Steve Witkoff and son-in-law Jared Kushner, was on its way to Islamabad after a refuelling stop in Paris.
The Iranian delegation, led by parliamentary Speaker Mohammad Baqer Qalibaf and Foreign Minister Abbas Araqchi, arrived on Friday.
Qalibaf on X said Washington had previously agreed to unblock Iranian assets and to a ceasefire in Lebanon, where Israeli attacks on Iran-backed Hezbollah militants have killed nearly 2000 people since the start of the fighting in March. He said talks would not start until those pledges were fulfilled.
Israel and the US have said the Lebanon campaign is not part of the Iran-US ceasefire while Tehran insists it is.
Qalibaf said separately that Iran was ready to reach a deal if Washington offered what he described as a genuine agreement and granted Iran its rights, Iranian state media reported.
The White House did not immediately comment on the Iranian demands, but Trump posted on social media that the only reason the Iranians were alive was to negotiate a deal.
"The Iranians don't seem to realise they have no cards, other than a short term extortion of the World by using International Waterways. The only reason they are alive today is to negotiate!" he said.
Vance, speaking as he headed to Pakistan, said he expected a positive outcome but added: "If they're going to try to play us, then they're going to find the negotiating team is not that receptive."
Islamabad was under an unprecedented lockdown on Saturday with thousands of paramilitary personnel and army troops on the streets ahead of what Pakistan Prime Minister Shehbaz Sharif called "make-or-break" talks.
Trump on Tuesday announced a two-week ceasefire in the war, which has halted US and Israeli airstrikes on Iran.
But it has not ended Iran's blockade of the Strait of Hormuz, which has caused the biggest-ever disruption to global energy supplies, or calmed the parallel war between Israel and Iran-backed Hezbollah in Lebanon.
Israeli ambassador to the US, Yechiel Leiter, and his Lebanese counterpart, Nada Hamadeh Moawad, will hold talks in Washington on Tuesday, Israeli and Lebanese officials said, amid the conflicting accounts on what those talks would cover.
Israeli attacks continued across southern Lebanon on Friday. One strike on a government building in the city of Nabatieh killed 13 members of Lebanon's state security forces, President Joseph Aoun said in a statement.
Hezbollah said in a statement on its Telegram channel that it fired rocket salvos at northern Israeli towns in response.
Hours after the ceasefire was announced, Israel launched the biggest attack of the war, killing more than 350 people in surprise strikes on heavily populated areas, Lebanese authorities said.
Tehran's agenda at the talks also includes demands for major new concessions, including the end of sanctions that crippled its economy for years.
It also wants acknowledgement of its authority over the Strait of Hormuz, where it aims to collect transit fees and control access in what would amount to a huge shift in regional power.
Iran's ships were sailing through the strait unimpeded on Friday, while those of other countries remained hemmed inside.
with DPA
