Salehi spoke outside of a 159-nation conference of the U.N.'s International Atomic Energy Agency that is expected to touch on fears over Tehran's nuclear aims.
Iranian President Hasan Rouhani is expected to affirm his commitment to trying to ease tensions in comments to the U.N. General Assembly this week.
Years of nuclear talks have been inconclusive and western negotiators seeking to curb programs that Tehran could turn from peaceful to military purposes have partially blamed disunity among top Iranian government figures.
Even with the recent installment of Rouhani and his relatively moderate aides, Ayatollah Ali Khamenei remains the top decision maker on the nuclear and other issues as the country's supreme leader.
But Salehi asserted the talks now had a better chance of succeeding because the new political leaders have a "more full-fledged ... desire" than their predecessors to reach agreement with the United States, Russia, China, Britain, France and Germany.
He described the new government as a "like-minded group ... that would facilitate the resolution of this issue if the other side comes with good intentions."
The United States, one of Iran's toughest critics, has welcomed Iran's more moderate tone under Rouhani and has urged Iranian officials to seize the moment in reducing nuclear tensions.
U.S. Energy Secretary Ernest Moniz, who heads his country's delegation to the Vienna conference, said Monday that Salehi's "words have to be followed by concrete actions."
A date and venue for the next round of talks is expected to be announced within the next few weeks.
In Tehran on Monday, state TV quoted Foreign Ministry spokeswoman Marzieh Afkham as warning that "threatening language against Iran" will backfire, adding: "Interaction with Iran will be possible only through respect."