Before the meeting, al-Maliki insisted that the security situation in Iraq was improving.
"The security situation ... has begun to develop tremendously, and the Baghdad of today is different from the Baghdad of yesterday," al-Maliki said after holding earlier talks with Ban.
The Iraqi leader also said his government would provide any necessary security for an expanded United Nations presence in his country.
The UN Security Council voted to assign the United Nations an expanded political role in Iraq last month, including promoting reconciliation between rival factions and dialogue with neighbouring countries.
"Iraq is still under foreign occupation and Iraqis continue to die in great numbers"
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But many UN officials are deeply concerned about sending more staff to Iraq, after a bomb that destroyed its office in Baghdad in August 2003 and killed 22 people, including mission chief Sergio Vieira de Mello.
The US and Britain have pushed for a bigger UN role in Iraq but deny they want to offload the problems facing their forces onto the world body.
The meeting on the sidelines of the UN General Assembly brings together Condoleezza Rice, the US Secretary of State with Manouchehr Mottaki, her Iranian counterpart, at a time of tension over Iran's nuclear ambitions.
And Al Jazeera's Kristen Saloomey in New York says that relations between Iraq and the US remain "very tense" after the Iraqi government said it was investigating a US security firm over the alleged killing of Iraqi civilians in a shooting incident.
The meeting will also review a five-year plan to stabilise the country on the political, economic and security fronts.
The talks also come in the wake of a damning report on Iraqi corruption by the US embassy in Baghdad that painted a grim picture of graft in all government departments.
But the White House said on Friday that al-Maliki was "working hard" to fight corruption but declined to say whether he had been "adequately successful."
On the meeting agenda are "challenges and opportunities" in implementing UN Security Council resolution 1770 adopted last month, as well as support for the Baghdad government's efforts to curb sectarian strife through an inclusive political dialogue and national reconciliation.
Resolution 1770 extended the mandate of the UN Assistance Mission in Iraq (UNAMI) by one year and urged it to "advise, support and assist" the Iraqi government on a wide range of issues.
Al-Maliki and representatives of Iraq's neighbours are also to examine how best to promote regional dialogue and cooperation, UN officials said.