Salih will "present the facts to our brothers in the Iranian leadership and clarify some misunderstandings so that relations are based on love and brotherhood," interim Prime Minister Iyad Allawi said.
"We have to start building clear and frank relations based on not interfering in the two countries' internal affairs," Allawi said in an interview with Iraq's state-run Iraqiya television, broadcast late on Saturday.
"There are negative elements and tensions which run contrary to the interests of both countries."
On arrival at the foreign ministry in Tehran, Salih explained the one-day delay in his trip by saying his direct flight to Tehran from Baghdad was the first in more than 25 years.
War of words
The visit comes amid an effort to ease a recent war of words between the two neighbours after several Iraqi officials joined the Americans in alleging Iran has been supporting fighters in Iraq and have been involved in a three-week-long Shia Muslim uprising in the south and centre of Iraq. The accusations included arming the fighters.
Iran has denied it is interfering and Foreign Ministry spokesman Hamid Reza Asefi told reporters that officials would focus the discussions on "Iranian nationals who are captive in Iraq".
An Iranian diplomat, Fereydun Jahani, went missing on 4 August on the road leading from Baghdad to Karbala in central Iraq where Tehran was set to open a consulate.
His kidnapping was claimed by a group calling itself the Islamic Army of Iraq. It was reported to have issued threats against him, but is not known to have carried them out yet.
Officials have said Salih is also due to prepare for a visit by Allawi.
No date has yet been set for Allawi's visit despite a formal invitation by Iran and trips to Iraq's other neighbours.