Miserable conditions endured by Syrian refugees and others in the Middle East as a result of the harshest weather for decades are set to worsen in the coming days as melting snow causes flooding.

Heavy snowfalls, torrential rain and icy winds have caused havoc, bringing down power lines, blocking roads and trapping people in homes and cars in Lebanon, Syria, Turkey, Jordan, Israel, Palestine and Egypt. Authorities in Jerusalem said the storm, named Alexa, was the worst to hit the city for 60 years.

Aid agencies warned that Syrian refugees living in tents and makeshift shelters faced desperate conditions, with the Bekaa Valley in Lebanon – where hundreds of thousands of people live in informal refugee settlements – particularly badly hit.

They expect to see a rise in respiratory infections, especially among the young and the old, burn injuries caused by makeshift fires, and chilblains and frostbite among the many whose feet are clad only in plastic flip-flops or sandals.

The Lebanese government, which has not set up properly run and equipped refugee camps for fear that their populations could become permanent, says the international community has failed to deliver on its promises of financial aid.

Al-Jazeera reported that there are at least 80,000 Syrian refugees in Lebanon living in tented settlements. These figures came from Dana Sleiman, a public information officer with the Office of the United Nations High Commissioner for Refugees (UNHCR). Hundreds of thousands more people are living in unfinished buildings, garages and other structures that offer little protection against the cold.

In Gaza, where around two-thirds of the 1.7 million population are classified by the United Nations as refugees dating from the 1948 war, serious flooding followed the first snowfall in around two decades. Thousands of people evacuated from their homes were sheltering in schools as the Gaza health ministry declared a state of "extreme emergency".

Jabaliya refugee camp, in the northern Gaza Strip, had "become a massive lake with two-metre-high waters engulfing homes and stranding thousands", according to Chris Gunness, of the UN agency for Palestinian refugees, Unrwa. "Large swaths of northern Gaza are a disaster area with water as far as the eye can see," he added.

Around 4,000 UN workers were evacuating families and distributing emergency supplies, including fuel to pumping stations. But Gunness said: "The situation is dire, and with the flood waters rising, the risk of waterborne disease can only increase. This is a terrible situation which can only get worse before it gets better."

In an indication of the severity of the situation, the Israeli military opened a border crossing to allow emergency supplies of heating gas into Gaza following an appeal by the UN. Four water pumps were also transferred into the blockaded territory to deal with flooding, the Israeli Defence Forces said.

Raw sewage mixed with flood waters was increasing the risk of disease. Gaza has been unable to pump sewage for more than a month, as power plants have shut down for lack of fuel. The fuel shortages – which were causing daily power cuts of 12-16 hours even before the crisis caused by storm Alexa – are mainly a result of the Egyptian authorities' destruction of most of the smuggling tunnels between Gaza and Egypt.

Jerusalem continues to be badly affected by snow, with the army clearing blocked roads and rescuing stranded motorists. Thousands of homes were without power on Saturday, and at least two people were reported to have died. Israeli authorities were forced to lift a Jewish sabbath public transport ban on Saturday and allow trains out of the city, where highways were shut to traffic.