Conditions in the region "compel us to have dialogue and co-operation between the two countries regarding the economy, investment, construction projects and security issues," Ahmadinejad said.
As well as meeting Karzai, the Iranian president will also hold talks with Younus Qanooni, speaker of the lower house of parliament and a key opposition figure, and some Iranian nationals.
The two presidents are likely to discuss Tehran's expulsion of thousands of Afghans living in Iran illegally. Around 170,000 unregistered Afghans have been forced to leave since April, causing an outcry in Kabul that cost the minister for refugees his job.
Karzai has always spoken positively of relations with Shia Muslim Iran, which was a staunch opponent of the government formed by the Sunni Muslim Taliban movement between 1996 and 2001.
But Washington, which is a key ally of Karzai's government and provides the majority of troops battling Taliban fighters, is critical of Tehran's involvement in Afghanistan.
On the eve of talks with George Bush, the US president, last week, Karzai described Iran as "a helper and a solution" to problems in the country, pointing to co-operation on security issues and drug enforcement.
Bush responded several days later by saying he "would be very cautious about whether or not the Iranian influence there in Afghanistan is a positive force".
Robert Gates, US defence secretary, said in June that given the large number of weapons coming into Afghanistan from Iran, it was hard to believe "that it's taking place without the knowledge of the Iranian government".
The charge has been strongly denied by Tehran.
Ahmadinejad's visit is his first to Afghanistan and follows Karzai's trip to Tehran in May 2006. He will travel to Turkmenistan and Kygyzstan after the meeting.