"The humanitarian situation is getting worse despite the scope of the operation increasing," said Peter Maurer, president of the International Committee of the Red Cross.
The Syrian Network for Human Rights, meanwhile said it documented 160 deaths Wednesday across the country, including 21 children and eight women. Three of the dead showed signs of torture, the organization said in a release.
Meanwhile, Assad told a Russian broadcaster he won't leave the war-ravaged country as suggested by Britain's prime minister, the BBC reported Thursday.
Assad's announcement came as Syria's fractured opposition groups met in Doha, Qatar, to discuss uniting under a new leadership body.
"I am not a puppet made by the West to go to the West or to another country," Assad said in remarks published on Russia Today TV's website. "I am Syrian. ... I must live and die in Syria."
If problems exist in Syria, "especially as we are the last bulwark of secularism, stability and coexistence in the region, then the domino effect of that would stretch from the Atlantic to the Pacific," he said.
Maurer said the conflict was causing more casualties and making it more difficult for the organization -- the only international aid agency with a presence inside Syria since fighting began March 2011 -- to reach victims in need of aid.
Maurer said there were "a lot of blank spots" and unknown numbers of people unable to access needed aid, the BBC said.
A Syrian medical group Wednesday claimed as much as 95 percent of foreign medical aid supplies had been funneled to government forces, which the ICRC said it couldn't substantiate, the BBC said.
Thursday's meeting of Syrian opposition groups in Doha was to bring together leaders of the Syrian National Council with other Syrian opposition elements, the broadcaster said. The main goal was to produce a unified, trustworthy opposition leadership that would be recognized by the Friends of Syria as the sole legitimate representative of the Syrians.
Meanwhile, Syria's armed opposition may be revamping its fighting strategy after having been driven back from Damascus during a government counteroffensive in the summer, the Los Angeles Times reported.
Observers said the new strategy seems to more closely resemble guerrilla strikes than fighting to maintain control already seized territory.
Also, rebels reportedly began attacks this week on a major pro-Assad Palestinian faction, the Times said. However, a rebel official denied the recent attacks were targeting specific sects.
"We don't do operations that hit or hurt the civilians, no matter their sect," said Abu Hadi, a spokesman for the Ahrar Houran brigade. "We are not sectarian and we don't think in terms of sectarianism."
Syria's state-run news agency reported Wednesday "an armed terrorist group" -- what the government has calls rebel forces -- assassinated a judge by using an explosive attached to his car. The brother of the parliamentary speaker was fatally shot Tuesday in his car in Damascus as he was going to work, state media reported.