The visit comes two days after Iraqi, Iranian and US officials held the first meeting of a committee aimed at improving co-operation on stabilising the country.
Although Iraq maintains warm relations with Iran, the United States has blamed Tehran for stoking the sectarian violence that has following the overthrow of Saddam.
Washington has accused Tehran of backing Shia militias and supplying weapons used against the US military in Iraq.
The charges have been denied by Iran.
|"The aim of the visit is to advance our bilateral relations and to discuss all issues of mutual concern including security, economic co-operation and trade"|
Hoshyar Zebari, Iraqi foreign minister
"The aim of the visit is to advance our bilateral relations and to discuss all issues of mutual concern including security, economic co-operation and trade," Hoshyar Zebari, Iraqi foreign minister, said on arrival.
Al-Maliki was met at Tehran's main city airport by Parviz Fattah, the energy minister, and headed to a welcoming ceremony attended by Parviz Davoudi, the vice president.
He was due to meet all of Iran's senior leaders during the three-day visit.
Al -Maliki flew to Tehran from Turkey where security had also dominated the agenda. He pledged to take "deterrent measures" against Kurdish fighters based in northern Iraq.
The prime minister - who lived in Iran during the 1980s to escape the persecution of his Dawa party during Saddam Hussein's war with Tehran - is under pressure from the US and members of his own cabinet.
Robert Gates, the US defence secretary, said on Sunday that he was disappointed with the lack of progress on reconciliation by al-Maliki and 17 ministers have quit or announced they are boycotting his cabinet.
The visit coincides with a meeting on Iraq's security being held in Syria which includes officials from Iraq, the US, Britain, Iran, Turkey and Jordan.
The two-day meeting is being held in a government complex on the outskirts of the capital Damascus.
One delegate said the talks would focus on ways to control the 360km border Syria shares with Iraq and dismantling alleged Iraqi Baathist networks in Syria.
"With all the talk of Syria as a transit route for rebels, it makes sense to hold the meeting here. This is a chance for Damascus to show it can co-operate and talk with US officials. The two sides rarely meet," the delegate said.
The Damascus meeting is a follow-up to a conference held in Egypt in May at which senior US and Syrian officials met each other for the first time in two years.