al-Assad "stressed the importance of international efforts focused on helping to rebuild infrastructure in Syria," the statement said.
More than 35,000 people were killed in Syria and Turkey after the tremor struck both nations on February 6, including more than 3,500 in Syria, officials and rescuers said.
Damascus often blames its financial woes on Western sanctions imposed in the wake of the 2011 conflict, that began with the brutal repression of peaceful protests and escalated to pull in foreign powers and global jihadists.
Despite the sanctions, government-controlled parts of the country receive international aid through UN agencies, many of which have headquarters in Damascus.
Griffiths also met Monday with Syrian Foreign Minister Faisal Mekdad in Damascus after visiting government-controlled Aleppo, where more than 200,000 people have been left homeless by the earthquake, according to the World Health Organization.
He told reporters in Aleppo that the UN was looking to raise money for the organizations helping Syrians cope with the disaster.
"The appeals that will go out in the next day or so - one for Syria, one for Turkey - will cover about three months of the humanitarian needs," he said.
Aid has been slow to arrive in Syria, where nearly 12 years of conflict have ravaged the healthcare system, and parts of the country remain under the control of rebels battling Assad's government.
Griffiths admitted Sunday that the UN had "so far failed the people in northwest Syria".
Before the earthquake struck, almost all of the humanitarian aid for the more than four million people living in rebel-controlled areas of northwestern Syria was being delivered from Turkey through the Bab al-Hawa crossing.
Aid delivery through Bab al-Hawa was interrupted by the quake but has since resumed, and calls to open other crossings are multiplying.
On Sunday, the head of the World Health Organization also met Assad and said that he had voiced openness to more border crossings for aid to be brought to quake victims in the country's rebel-held northwest.
Up to 5.3 million people in Syria may have been made homeless by the devastating earthquake which rocked the region, according to the UN.
al-Assad Asks for Quake Aid
FILE - Syrian President Bashar al-Assad, right, shakes hands with Turkish Prime Minister Recep Tayyip Erdogan during a meeting in Aleppo, Feb. 6, 2011. Both nations have been hit by a massive earthquake that has killed more than 35,000. (AFP Photo/HO/SANA
Syrian President Bashar al-Assad called Monday for international aid for reconstruction in the quake-struck country during a meeting with United Nations relief chief Martin Griffiths, the presidency said.
DAMASCUS —