Saturday's talks produced spare formal statements in public but were charged with significance, touching on competition between Washington and Tehran for influence in Iraq and on Chalabi's volatile personal ties to the Bush administration.
Ahmadinejad, quoted on Sunday by the official IRNA news agency, blamed the U.S. occupation for violence in Iraq and said he expected the vote on Dec. 15 to produce a strong government.
Chalabi, IRNA said, called for closer trade ties with Iran.
But though the comments made by both sides were routine, the visit itself was full of intriguing potential; the recently elected Ahmadinejad is at daggers drawn with Washington over Iran's nuclear programme, but is an influential ally of fellow Shi'ite Islamists running Iraq's U.S.-backed government.
Chalabi, a favourite of the Pentagon when he worked from exile against Saddam Hussein, fell out with his patrons last year, partly over their accusations that he leaked U.S. secrets to Tehran.
A secular Shi'ite, he joined the main Islamist-led bloc that took control of Iraq's parliament in an election in January. But last month he broke with the Alliance, and he is now campaigning on his own Iraqi National Congress ticket.
U.S. officials, briefing reporters anonymously, have given seemingly contradictory signals about the significance of next week's visit by Chalabi to Washington, his first in a year.
Chalabi himself said last week it showed there was no "wall of ice" between him and the Bush administration.
Some appear to indicate that his rehabilitation in favour could go so far as to make him an acceptable candidate to be prime minister in U.S. eyes, an alternative to the Islamists whose ties to Iran go back to their long years in exile.
Other U.S. officials have played down the visit, expected to include meetings with Secretary of State Condoleezza Rice and Treasury Secretary John Snow, calling it a business trip related to Chalabi's work with Iraq's budget and oil industry.
Chalabi's personal political base seems small but he has shown a flair for building alliances, including with the Shi'ite Islamists who dominate the majority community's politics, propelling himself to the position he holds today.
Ahmadinejad, whose country denies U.S. accusations of stirring up unrest in Iraq, said the violence was "the tragic outcome of the occupation by foreign forces", IRNA said.
"Insecurity is an excuse for the continuation of the presence of U.S. forces in the region."
Separately, the agency quoted Chalabi as saying on Saturday: "The Islamic Republic of Iran plays a very constructive and positive role in (the) formation of (an) Iraqi government."