The head of the group, lawmaker Khaled al-Attiyah, said upon arriving at the airport on Thursday that the "new Iraq" will not allow anything to threaten the ties between the two countries and disagreements should be solved through "dialogue and coordination".
Hundreds of Iraqis demonstrated at the frontier late last month to protest against a metal barrier Kuwait is building, and Iraqi legislators on Tuesday - the 15th anniversary of Iraq's invasion of this country - accused Kuwait of chipping at Iraqi territory and stealing Iraqi oil.
Iraqi demonstrators fired several shots into Kuwait, but no one was injured and Kuwaiti border guards did not return fire. Construction of the barrier has temporarily halted.
The United Nations redrew the border after the 1991 Gulf war that liberated Kuwait from a seven-month Iraqi occupation under former leader Saddam Hussein.
It placed 11 oil wells, some farms and an old naval base that used to be in Iraq on the Kuwaiti side.
"In the name of the prime minister ... I assure you that this method [dialogue] will be implemented and misunderstandings and the causes of the problems will be gone," al-Attiyah said.
Al-Attiyah said he would talk to Kuwaiti officials about "some [border] matters that have not been resolved yet". He did not elaborate.
Kuwait, which was the launchpad for the US-led war that toppled Saddam, says the UN border demarcation of 1993 is final, but that it is open to talks with Baghdad.
"In the name of the prime minister ... I assure you that this method (dialogue) will be implemented and misunderstandings and the causes of the problems will be gone"
It says some Iraqi farms and homes in the border area of Umm Qasr have "encroached" into Kuwait.
Many farms in the same area were razed following the post-Gulf war demarcation. Kuwait's Foreign Minister Muhammad al-Salim Al Sabah said in remarks published in Al-Anba on Thursday that Kuwait had deposited compensation for those farmers in a UN fund.
The minister, who met with top editors of local dailies to speak about the tensions, denied accusations by Iraqi lawmakers that Kuwait was digging horizontal oil wells to pump Iraqi oil.
The allegations were similar to those used by Saddam to justify the invasion.
Relations between Iraq and Kuwait resumed after the 2003 US-led invasion of Iraq and border points were reopened.
When Saddam was still in power, Kuwait built a defensive trench along the 210-km border to stop infiltration from both sides.
UN peacekeepers patrolled the frontier until just before the invasion of Iraq.