Red Cross says it cannot cope with Syria emergency
The Red Cross has said it "can't cope" with the worsening situation in Syria.
"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 (ICRC).
Meanwhile, President Assad has told Russian TV that he will not leave Syria as suggested by the UK prime minister.
It comes as Syria's divided opposition groups are meeting in Doha to discuss uniting under a new leadership body.
"I am not a puppet, I wasn't made by the West. I'm Syrian... and I have to live and die in Syria," Mr Assad told the Russia Today TV channel.
He warned that if Syria were to be invaded by foreign troops "the price would be too big" for the rest of the world.
"If we have a problem in Syria - and we are the last stronghold of secularism, stability and co-existence in the region - it will have a domino effect from the Atlantic to the Pacific.
He said he believed the West wouldn't move in that direction, but added: "If they do so, nobody can tell what's (going to happen) next."
Mr Maurer said the conflict was causing more casualties and making it difficult for the ICRC to reach victims.
There are currently "a lot of blank spots" and an unknown number of people were not getting access to the aid they needed, Mr Maurer added.
The ICRC has not been able to get to certain parts of the country, he added, giving as an example the city of Aleppo, which has been badly hit by violence in recent months.
Its personnel were able to access some districts of the flashpoint city of Homs last week, which Mr Maurer said was a major success.
The constantly moving nature of the conflict meant the Red Cross could not plan but instead had to seize opportunities for aid delivery on a day-to-day basis, Mr Maurer said.
His comments come a day before UN diplomats and aid agencies are due discuss the issue of access to Syria at a meeting in Geneva.
On Wednesday, a Syrian medical group claimed that up to 95% of foreign medical aid supplies were being diverted into the hands of government forces - a statement that the ICRC says is so far unsubstantiated, the BBC's Imogen Foulkes in Geneva reports.
The meeting of Syrian opposition groups on Thursday is set to bring together leaders of the Syrian National Council, hitherto the main opposition group, with other Syrian opposition elements.
The meeting will take place under the auspices of the Arab League, with Western powers from the international Friends of Syria group also taking part.
The key objective is to produce a unified, credible opposition leadership firmly rooted inside Syria itself, which would then be recognised by the Friends of Syria as the sole legitimate representative of the Syrians, the BBC's Jim Muir reports from Doha.
Few expect that to be achieved in one day of talks, so the meeting could be the beginning of a longer process. However, there is strong pressure to produce swift results, he adds.
The SNC's failure to present a united front against President Assad has previously brought widespread criticism.
The US has said it wants to set up a broader opposition leadership council in which the SNC's influence is diluted.
The Syrian National Initiative, proposed by prominent dissident Riad Seif, would supplant the SNC and bring together Syria's exiled and internal opposition, allowing it to become the conduit for foreign assistance.
Also on Thursday, the Israeli military said at least one mortar landed in the Israeli-occupied Golan Heights. No damage or injuries were reported.
In recent days, an Israeli border patrol vehicle was been hit by Syrian gunfire in the Golan Heights and three Syrian tanks entered the demilitarised buffer zone, the Israeli military say.