“We still need to do much more to reach all those who need help in order to avoid the risk of waterborne diseases spreading,” Youssouf Abdel-Jelil, a Unicef representative in Damascus, said in a statement.

The latest crisis statistics from the United Nations came as Damascus was gripped in the third consecutive day of clashes between insurgents and loyalists to President Bashar al-Assad. Activist groups have described it as the worst violence there in months, but there was no indication that rebel fighters were any closer to gaining control of the capital, which is heavily defended.

The Syrian Observatory for Human Rights, an anti-Assad group based in Britain with a network of contacts in Syria, reported that at least 50 civilian workers from a defense factory were killed in a bus bombing on Wednesday near the central city of Hama — more than double the toll the group had said earlier. It attributed the delay in reporting the updated number to an inability to get information from the area, which is controlled by the government.

Syria’s state-run news media reported what it described as a terrorist bombing near Hama but did not specify casualties. It is unclear who was responsible for the blast.

Mr. Edwards, in Geneva, said that as of this week, 787,000 Syrians had registered or were waiting to register as refugees in neighboring countries. The total includes 260,943 in Lebanon, the first country to exceed a quarter-million Syrian refugees; 242,649 in Jordan; 177,180 in Turkey; and 84,852 in Iraq. At least 15,000 have sought refuge in Egypt.