Despite the attacks, violence overall has reportedly decreased across Iraq.
'Back from the abyss'
Opening the one-day conference, Ban Ki-moon, the UN secretary-general, said: "Iraq is stepping back from the abyss that we feared most."
For his part, al-Maliki said: "We call on our brothers, friends and partners ... to commit to supporting Iraq's sovereignty and banning interference in its internal affairs and to end the international sanctions that were imposed on Iraq because of the previous regime and to write off debts."
Oil exports are also on the rise but al-Maliki's government says it needs more support to supplement its political and security gains.
The Stockholm conference was called to assess Iraq's progress a year after the International Compact with Iraq (ICI), a five-year plan adopted to bring peace, prosperity and political reconciliation to the war-torn country, was signed in Egypt.
At that meeting, officials from 50 countries promised to cancel $32bn of Iraq's foreign debt.
Western nations, Japan and commercial creditors have cancelled $66bn worth of debt over the past three years.
Iraq is still in talks with Arab Gulf states for further debt relief, with around $67bn remaining in oustanding debts.
In his speech on Thursday, al-Maliki said Iraq needs to get rid of the burden of war reparations and debt which he called "an impediment against reconstruction and development".
Clayton Swisher, Al Jazeera's correspondent in Stockholm, said: "Out of more than 90 nations representative [at the conference] in Sweden, observers say it's the United States and Iran who may hold the most sway over Iraq's future.
"No direct talks are expected today between the two. And many feel that until that happens, real progress in Iraq will remain elusive."
Condoleezza Rice, the US secretary of state, said that the world needed to support the rebuilding of Iraq, now that it is in a "fundamentally different" situation then it was a year ago.
Still, on the ground, political divisions in Iraq have flared recently.
The main Sunni Arab political bloc, which quit the government in August, said on Wednesday it suspended talks to rejoin al-Maliki's administration after a disagreement over a cabinet post.
Additionally, no Arab country currently maintains a permanent ambassador in Baghdad. Arab governments cite security concerns.
Sweden, which did not take part in the US-led invasion of Iraq in 2003 and hosts a large community of Iraqi refugees, has said that neighbouring Arab nations need to engage more with the Iraqi government to give reconstruction efforts a chance of success.
Swedish officials have cautioned against expecting "a major breakthrough" at the Stockholm meeting.
Washington too has played down expectations.
Several demonstrations are planned around the conference centre and across Stockholm against the continued US presence in Iraq.