The departure of the Austrians, announced Thursday, has threatened the future of the Golan peacekeeping force, known as the United Nations Disengagement Observer Force, or Undof, a multinational group of about 1,000 soldiers who have helped keep the area relatively tranquil for four decades.

The Austrian government decided to pull its 380 soldiers on Thursday after Syrian rebels briefly seized the Austrian area of responsibility, the Quneitra crossing between Israel and Syria, in clashes with Syrian government forces that lasted for several hours.

United Nations officials declined Mr. Putin’s offer. “We appreciate the consideration that the Russian Federation has given to provide troops to the Golan,” said Martin Nesirky, a spokesman for Secretary General Ban Ki-moon. “However, the disengagement agreement and its protocol, which is between Syria and Israel, do not allow for the participation of permanent members of the Security Council in Undof.”

The United Nations believes that one-third of Syria’s 20 million people need assistance urgently and that the number could rise to 10 million by the end of the year. At the same time, relief agencies are struggling to keep up with an outflow of 200,000 refugees every month, said Mr. Guterres, the refugee commissioner.

The United Nations puts the current number of refugees at 1.6 million and says that if the fighting does not stop, the number could double by the end of the year.

In response, the United Nations called for $2.9 billion in 2013 to support refugees and $1.4 billion for people trapped inside the country. It also asked for $830 million on behalf of Lebanon and Jordan, which have more than half a million registered refugees each and many more unregistered ones.

The United Nations-coordinated response has already received about $1.25 billion from appeals earlier this year, United Nations officials said.