Mr Al Kadhimi has served in a caretaker role since a general election last October, as Iraqi political factions continue to squabble over forming a government.
"My government has called for a serious and transparent dialogue between all political forces and parties to discuss ways out of the current political crisis in an effort by the government to meet the people's aspirations and hopes, and achieve their goals to secure our people's future," he told the UN General Assembly.
Mr Al Kadhimi, who has been in office since May 2020, told the Iraqi News Agency before his speech that Iraq's problems would not be solved without dialogue and that political factions have an opportunity to rebuild the country.
"The government of Iraq is working to build the state to maintain its structure on the basis of coexistence among all the Iraqi people," he declared in his UN speech.
He also emphasised how the stability of the region relies on the stability of Iraq, and any internal conflicts also have an impact globally.
"Iraq is keen to be a source of stability regionally and internationally," he said.
"Iraq seeks to bring together different viewpoints and endeavours to find sustainable peaceful solutions to regional crises and mend ties between the region's countries by introducing a number of initiatives to ensure peace and security in our region, a region that has long suffered from wars and crises."
The Iraqi prime minister made his remarks as his country continues to face political deadlock, with the main political actors preventing parliament from selecting a new speaker, president and prime minister.
Shiite cleric Moqtada Al Sadr's followers became the largest bloc in parliament after the October elections, with 73 seats, but fell far short of a majority.
After the rival, Iran-aligned Co-ordination Framework frustrated his attempts to form a government, Mr Al Sadr called for fresh elections.
The Co-ordination Framework wants a new government to be installed first to oversee the election.
The dispute between the two largest Shiite blocs resulted in violent clashes on the streets of Baghdad and cities in the south of the country last month.
In an exclusive interview with The National ahead of his General Assembly address, Mr Al Kadhimi said there was no way out but to pursue dialogue among political groups.
He said the dialogue he was convening was primarily focused on holding new elections, coupled with a new “compact” to ensure all sides respect the results.
“A thousand years of dialogue is better than one moment of killing,” he said in an interview in New York.
He said it was time to “divorce the violent past and a future built on true democratic values built not just on the ballot box votes”.
His comments came as authorities said they had arrested a person who confessed to killing protesters last month.
“Last week, we arrested a person, who belongs to one of the state institutions, who confessed to killing protesters and some personalities,” Mr Al Kadhimi said.
Hundreds of protesters were injured and dozens killed during last month's protests over the political stand-off.