Kadhimi, who is on his first visit to Iran as prime minister, said that he "won't allow any aggression or challenge to Iran from its territory".
He also alluded to Iran now using Iraq as a battleground for its proxy war against the US, during a televised conference with Iranian President Hassan Rouhani.
"The people of Iraq want good relations with the Islamic Republic of Iran based on the principle of non-interference in the internal affairs of both countries," he said, according to Reuters.
It comes as the new prime minister seeks to balance power in Iraq between his foreign allies, the US and Iran - who are both engaged in a bitter deadlock \- and further the authority of the Baghdad government.
Tehran wields enormous power and influence in Iraq through a vanguard of Revolutionary Guards commanders, local militias, and allied politicians.
Iran-linked militias have carried out numerous attacks on US forces based in Iraq, while Washington assassinated Iranian General Qassem Soleimani in January this year at Baghdad Airport.
The killing led to retaliatory missile strikes by Iran on US bases in Iraq, threatening to engulf the country in another bloody conflict.
Kadhimi has sought to curb the powers of some powerful Iraqi Popular Mobilisation Forces militia coalition since he took over as premier in May.
Iran’s hardliner Supreme Leader Ayatollah Ali Khamamenei praised the PMF after a meeting with Kadhimi on Tuesday.