"Yes, we have mutual interests, and there are real challenges, we have to combine our stances to solve problems and to weave a network of good relations for both countries," al-Maliki responded.
The visit is al-Maliki's first visit to Syria since he became prime minister early last year.
The Iraqi prime minister lived in the country in the 1990's as an exile from Saddam Hussein's reign.
The United States, which has already criticised a similar trip by al-Maliki to Iran earlier this month, said it hoped the he was delivering a "strong message" to the Syrian leadership about the role of Damascus in Iraq.
|"We have to combine our stances to solve problems and to weave |
a network of good relations"
Iraqi prime minister
Washington has accused Damascus of not doing enough to prevent Sunni fighters from crossing over into Iraq.
Damascus said earlier this month that it had taken measures on its eastern border to increase security.
Border patrols have been increased, restrictions people under 30 crossing the border tightened and large number of infiltrators arrested, it said.
On Monday, Naji Ottri, the Syrian prime minister, said US coalition forces in Iraq were most responsible for the security deterioration and said their withdrawal was key to national reconciliation.Iraqi refugees
Al-Maliki is also expected to meet some of the estimated 1.5 million to two million Iraqi refugees who have to Syria.
The UN High Commissioner for Refugees (UNHCR) said last month that health and education services in Syria and Jordan were struggling to cope with the amount of Iraqi refugees.
Al-Maliki told al-Assad that Iraq takes "into consideration the pressures Syria is facing," while the Syrian leader said Damascus was "ready to offer everything helping in Iraq's stability".
Iraq and Syria restored diplomatic ties in November after a 26-year break over Syria's support for Iran in its eight-year war with Iraq.
The reopening of an oil pipeline which was closed after the two country's cut ties in 1980.