Thousands flee Syria

• "The humanitarian situation is deteriorating fast," an ICRC spokeswoman says
• U.N. official: More than a million people are displaced; another million need urgent aid
• The Syrian regime has said it is worried about aid getting into the hands of "terrorists"

(CNN) -- The head of the Red Cross is negotiating with Syrian officials this week for better access to civilians besieged by the country's bloody civil war.

Peter Maurer, president of the International Committee of the Red Cross, met Tuesday with Syrian President Bashar al-Assad, an agency spokeswoman said.

Maurer will meet with other officials Tuesday and Wednesday and might give a briefing of his talks later this week, spokeswoman Cecilia Goin said.

The flow of aid has hardly kept up with the pace of violence in war-torn Syria, with scores or hundreds of people reportedly killed each day. Medics resort to makeshift clinics and crude supplies to treat the wounded, sometimes without electricity.

Goin said the ICRC is already helping thousands of people across Syria, including displaced residents. But some of the most desperate civilians remain trapped in relentless violence.

"In those places where fighting is taking place, it's very hard to access those people in need," Goin said.

"The humanitarian situation is deteriorating fast."

During her trip to Syria last month, U.N. humanitarian chief Valerie Amos offered a grim account of the civil war's toll on the masses: more than a million uprooted; a million more in need of urgent aid.

Amos said she is "extremely concerned that all parties of the conflict are failing to comply with international humanitarian law, which sets out clear rules on the protection of civilians."

"This conflict has taken on a particularly brutal and violent character," she said after visiting Damascus.

The Syrian government estimated that 1.2 million people are sheltering in public buildings, and "many more are staying with relatives and friends," Amos said. "Both those who have fled and their hosts have urgent humanitarian needs due to the widening impact of the crisis on the economy and on people's livelihoods."

Al-Assad's regime has said it will let aid groups already in the country expand their operations but won't allow new aid to enter.

The government is worried the aid would get into the hands of "armed groups and terrorists," a phrase it has used to describe those seeking al-Assad's ouster.

The United Nations and its partners are reaching more people each month with food and emergency aid, Amos said. In July, more than 820,000 people were fed, and in the first two weeks of August, basic necessities such as hygiene kits and blankets were distributed to more than 60,000 people.

Goin, the ICRC spokeswoman, said the group has previously asked for a cease-fire to deliver aid. But bloodshed across the country has only intensified since.

"The national authorities and the armed opposition groups, they must respect and help facilitate" access by aid workers, Goin said. "The only goal of the organization is humanitarian."