Israel and the U.S. have said the Lebanon campaign is not part of the Iran-U.S. 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 realize 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."
Preliminary discussions have been separately held by Pakistani officials with advance teams from both sides, sources in Islamabad said.