Salehi, who oversees Iran's controversial nuclear programme, was named as interim foreign minister after his predecessor, Manouchehr Mottaki, was sacked by President Mahmoud Ahmadinejad on December 13.
"Iran's first priority in diplomacy should be neighbours and the Islamic world. In this regard, Saudi Arabia and Turkey have a special position," Salehi, a fluent Arabic and English speaker, was quoted as saying by Mehr news agency after he took charge of the ministry.
"Saudi Arabia deserves to have special political ties with Iran. Iran and Saudi Arabia, as two effective countries in the Islamic world, can resolve many problems together."
Salehi's remarks about Saudi Arabia are significant after US diplomatic cables released by WikiLeaks showed Riyadh obsessed by a threat from Iran. King Abdullah reportedly urged top US officials to destroy Tehran's nuclear programme, telling them "to cut off the head of the snake."
Ties between Iran and Turkey have grown in recent months with Ankara even endorsing a nuclear fuel deal for Tehran in May, along with Brazil.
Turkey is also hosting the next round of talks between Iran and the six world powers in Istanbul, following the last negotiation held in Geneva on December 6 and 7. Turkey has repeatedly called for sustained diplomacy to resolve Iran's nuclear controversy.
"Turkey is a powerful country with strategic position and shares common cultural and ideological grounds with Iran," Salehi said.
Salehi, 61, said Iran and the European Union too would "benefit" if the EU switched its position towards Tehran from "confrontation to engagement as soon as possible."
"Despite some unfair moves by the European Union, this union wants respectful ties with Iran for a number of reasons, including energy," he said.
Salehi also underlined the importance of expanding ties with Syria, Iraq, Azerbaijan, Afghanistan and Pakistan, and Russia and China.
Salehi took charge at a function that was also the farewell ceremony for Mottaki. However, the 57-year-old Mottaki, who was fired while he was on an official visit to Senegal, did not attend.
His dismissal came after he hailed as a "step forward" remarks by US Secretary of State Hillary Clinton that Iran is entitled to a peaceful nuclear energy programme.
Clinton had told the BBC Tehran could enrich uranium for civilian purposes in the future, but only once it has demonstrated it can do so in a responsible manner and in accordance with Iran's international obligations.
Mottaki's comments appeared to cut across Iran's official position, repeated almost daily, that its enrichment of uranium is non-negotiable.
Mottaki's sacking also came just days after Iran held talks in Geneva with world powers over the nuclear dossier.
Salehi, who was appointed atomic energy chief on July 17, 2009, has been a driving force behind Iran's atomic programme. During his tenure, the country's first nuclear power plant built by Russia has come on line in the southern city of Bushehr.
Before taking up the post, he was deputy chief of the Jeddah-based Organisation of the Islamic Conference.
Salehi holds a doctorate from the prestigious Massachusetts Institute of Technology.
He served as Tehran's representative at the Vienna-based International Atomic Energy Agency during the presidency of reformist Mohammad Khatami.
Media reported that Salehi will be interim foreign minister until parliament endorses his appointment.
Meanwhile, Vice President Mohammad Reza Rahimi said Salehi's appointment comes at a time when Iran was at a "special and crucial" position following the sanctions.
"It is now Mr Salehi's turn to launch a new initiative following Mr Mottaki's efforts and do a greater job for the system," he was quoted by ISNA news agency as saying.
The United Nations Security Council imposed the fourth set of sanctions on Iran on June 9, which were followed by unilateral punitive measures by the EU, the United States and several other countries.
TEHRAN — By Jay Deshmukh (AFP)