Hamas has previously said that Israel was required to allow in about 300,000 tents and 60,000 caravans during the six-week-long first phase of the deal.
Israeli military body Cogat said Israel was "committed to and complies with the obligation to allow the entry of 4,200 humanitarian aid trucks per week" into Gaza, including those carrying tents and shelter supplies.
"Based on the data available to us, hundreds of thousands of tents have entered the Gaza Strip since the agreement came into effect," it added.
Babies between 2 and 4 lbs, so tiny require warmth. The temperature at night is around 3 or 4 degrees.