The two premiers then met in "a positive atmosphere" and discussed steps to deal with outstanding issues in relations, said Ali Moussawi, a Maliki adviser.
"The two sides showed their insistence on developing relations, and getting over problems of borders and economic and security files," he said.
They agreed to form a committee to address outstanding issues, which will be jointly headed by the countries' foreign ministers, Moussawi said.
"The committees will meet soon, to find solutions via dialogue," he said.
Kuwaiti Foreign Minister Sheikh Mohammed Sabah al-Salem al-Sabah, who accompanied Sheikh Nasser, said at a news conference that "there are several issues the Iraqi-Kuwaiti committee will discuss, including the issue of debts."
He added that Kuwait is interested in investing in Iraqi infrastructure: "We have a real desire to set up bridges between two peoples, and there is a big Kuwaiti desire for investment in Iraqi infrastructure," he said.
Sheikh Nasser's visit is the first by a Kuwaiti premier to Iraq since Sheikh Saad al-Abdullah al-Sabah visited in 1989. In August 1990, Iraq's Saddam Hussein ordered his forces to invade Kuwait.
The invasion was quickly met with a concerted international military response that seven months later pushed Saddam's forces out of the emirate.
The dictator was ousted by a US-led coalition in 2003.
Moussawi said Kuwait also expressed support for an Arab summit set for Baghdad in March, in which the country will be represented by its emir, Sheikh Sabah al-Ahmad al-Sabah.
"Kuwait expressed its desire for the summit to succeed, and will participate in it, represented by the emir of the country, and will make efforts to support Iraq in getting out of Chapter Seven," he said.
That was a reference to the section of the UN Charter under which sanctions were imposed on Iraq.
Sheikh Nasser's visit comes two days after a Kuwaiti coastguard was killed during a clash with Iraqi fishermen in which the Iraqis' boat was sunk.
Kuwait's interior ministry said the skirmish occurred when an Iraqi boat entered Kuwaiti waters and refused orders from a coastguard patrol to stop.
There are a number of outstanding issues between Iraq and Kuwait relating to the Iraqi invasion and occupation of Kuwait.
Iraq still pays 5% of its oil sales into a reparations fund for Kuwait, which is demanding that Baghdad pay another $22 billion. Kuwait has received about $13 billion so far.
Kuwait also demands that Iraq return property stolen during the occupation and explain the fate of hundreds of missing Kuwaitis.
In December, the emirate urged Iraq to fully apply all international resolutions and settle outstanding issues after the UN Security Council voted to end key sanctions imposed on Baghdad.
At the time, the Kuwaiti cabinet also welcomed Security Council resolutions to halt some sanctions that were imposed on Iraq after the 1990 invasion.
Kuwait said "commitment to serious and full implementation of Security Council resolutions related to the situation between Iraq and Kuwait will close all files and settle outstanding issues.
"This will also lay foundations for strong relations based on the respect of sovereignty and independence and the principle of good neighbourly relations and non-interference in internal affairs," it said.
In August, Kuwait and Iraq agreed in principle on a deal to regulate production from the border oilfields that were at the centre of their war.
A number of oilfields lie on the border between the two Arab countries, including Iraq's giant Rumaila field which extends into Kuwait, where it is known as Ritqa. There are other such fields in Zubair and Safwan.
Saddam accused Kuwait of stealing oil from Rumaila when his forces launched their invasion.
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"The two sides showed their insistence on developing relations, and getting over problems of borders and economic and security files," he said.
They agreed to form a committee to address outstanding issues, which will be jointly headed by the countries' foreign ministers, Moussawi said.
"The committees will meet soon, to find solutions via dialogue," he said.
Kuwaiti Foreign Minister Sheikh Mohammed Sabah al-Salem al-Sabah, who accompanied Sheikh Nasser, said at a news conference that "there are several issues the Iraqi-Kuwaiti committee will discuss, including the issue of debts."
He added that Kuwait is interested in investing in Iraqi infrastructure: "We have a real desire to set up bridges between two peoples, and there is a big Kuwaiti desire for investment in Iraqi infrastructure," he said.
Sheikh Nasser's visit is the first by a Kuwaiti premier to Iraq since Sheikh Saad al-Abdullah al-Sabah visited in 1989. In August 1990, Iraq's Saddam Hussein ordered his forces to invade Kuwait.
The invasion was quickly met with a concerted international military response that seven months later pushed Saddam's forces out of the emirate.
The dictator was ousted by a US-led coalition in 2003.
Moussawi said Kuwait also expressed support for an Arab summit set for Baghdad in March, in which the country will be represented by its emir, Sheikh Sabah al-Ahmad al-Sabah.
"Kuwait expressed its desire for the summit to succeed, and will participate in it, represented by the emir of the country, and will make efforts to support Iraq in getting out of Chapter Seven," he said.
That was a reference to the section of the UN Charter under which sanctions were imposed on Iraq.
Sheikh Nasser's visit comes two days after a Kuwaiti coastguard was killed during a clash with Iraqi fishermen in which the Iraqis' boat was sunk.
Kuwait's interior ministry said the skirmish occurred when an Iraqi boat entered Kuwaiti waters and refused orders from a coastguard patrol to stop.
There are a number of outstanding issues between Iraq and Kuwait relating to the Iraqi invasion and occupation of Kuwait.
Iraq still pays 5% of its oil sales into a reparations fund for Kuwait, which is demanding that Baghdad pay another $22 billion. Kuwait has received about $13 billion so far.
Kuwait also demands that Iraq return property stolen during the occupation and explain the fate of hundreds of missing Kuwaitis.
In December, the emirate urged Iraq to fully apply all international resolutions and settle outstanding issues after the UN Security Council voted to end key sanctions imposed on Baghdad.
At the time, the Kuwaiti cabinet also welcomed Security Council resolutions to halt some sanctions that were imposed on Iraq after the 1990 invasion.
Kuwait said "commitment to serious and full implementation of Security Council resolutions related to the situation between Iraq and Kuwait will close all files and settle outstanding issues.
"This will also lay foundations for strong relations based on the respect of sovereignty and independence and the principle of good neighbourly relations and non-interference in internal affairs," it said.
In August, Kuwait and Iraq agreed in principle on a deal to regulate production from the border oilfields that were at the centre of their war.
A number of oilfields lie on the border between the two Arab countries, including Iraq's giant Rumaila field which extends into Kuwait, where it is known as Ritqa. There are other such fields in Zubair and Safwan.
Saddam accused Kuwait of stealing oil from Rumaila when his forces launched their invasion.
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