ICRC spokewoman Rabab al-Rafai did not give further details about Assad's meeting with Peter Maurer, but said the Red Cross chief later met with Deputy Foreign Minister Faysal Mekdad and was also holding talks with the head of the Syrian Arab Red Crescent, Abdul-Rahman Attar.
"President Assad confirmed Syria welcomes the humanitarian operations that the organization is conducting on the ground in Syria as long as it works in a neutral and independent way," the state-run SANA news agency quoted Assad as saying.
Maurer's three-day visit, which began Monday, comes as the need for humanitarian assistance in Syria has grown increasingly urgent with the fighting having spread to the country's two largest cities — the capital Damascus and the commercial hub of Aleppo. Activists say August was the bloodiest month since the uprising against Assad began in March 2011, with about 5,000 people killed.
The escalating bloodshed has prompted a growing exodus by Syrians looking to escape the conflict.
The U.N.'s refugee agency, UNHCR, said Tuesday that 100,000 refugees fled Syria to neighboring countries in August, the highest monthly toll since the crisis began. In Geneva, agency spokeswoman Melissa Fleming said the rise in people seeking asylum in neighboring countries brings the total of Syrian refugees registered or awaiting registration with the UNHCR to 234,368 as of September 2.
The Red Cross said earlier that during his trip Maurer would address the "rapidly deteriorating humanitarian situation" and the difficulties which the ICRC and the Syrian Arab Red Crescent face in reaching people affected by the country's civil war.
"At a time when more and more civilians are being exposed to extreme violence, it is of the utmost importance that we and the Syrian Arab Red Crescent succeed in significantly scaling up our humanitarian response," Maurer said in comments made before his arrival in Syria. "An adequate humanitarian response is required to keep pace with needs, which have been growing exponentially."
Maurer added that during his visit, he also intended to follow up on points agreed to in April, such as expanded access to persons detained in Syria and "the imperative necessity of helping civilians affected by hostilities."
Syria's uprising began with largely peaceful protests against Assad's regime, but has since morphed into a civil war in the face of a brutal government crackdown. Activists say at least 23,000 people have been killed so far.
The civil war witnessed a turning point in July when rebels carried out an audacious bombing in Damascus that killed four high-ranking security officials, including the defense minister and Assad's brother-in-law. Since then, the regime has succeeded in largely quelling a rebel offensive in the capital, but has struggled to contain an opposition push into the northern city of Aleppo, the country's commercial hub.
On Tuesday, Abdul-Qadir Saleh, the commander of the Tawhid Brigade that is spearheading the Aleppo offensive, said rebels now control most of the city, Syria's largest.
"The regime only controls 30 percent of Aleppo," Saleh told reporters in Istanbul. He added that regime forces are now attacking civilian areas in an attempt to "turn civilians against the rebels."
Saleh's claim could not be independently verified, and the government says its troops are advancing in the city.
Also Tuesday, activists reported scattered violence across the country, including in Aleppo and Idlib in the north, Daraa in the south as well as the Damascus suburbs.
Associated Press writer John Heilprin in Geneva contributed to this report.