According to Hamas, these understandings include improvements to the water and electricity supplies, relaxed rules on imports and exports to Gaza, and the expansion of industrial projects.
The understandings are part of a developing internationally brokered agreement to calm frequently flaring violence between Israel and Hamas in Gaza.
Shortly after the announcement, a fire broke out in an Israeli greenhouse close to the Gaza border. The blaze caused some damage but no injuries.
Investigators are exploring whether the fire was started by one of the incendiary balloons sent from Gaza that have caused massive fire damage to Israeli fields and woodlands nearby.
The Qatari delegation entered Gaza on Sunday night, delivering $15 million in relief funds, according to reports. Another $10 million was transferred to Israel to fund the purchase of fuel for Gaza's power plant.
The Palestinian media reported that Khaled Al-Khardan, deputy to envoy Mohammed Al-Emadi, entered the Strip at the head of the delegation after El-Emadi was delayed in Israel in order to continue talks with Israeli authorities. He eventually arrived in Gaza around 10:30 pm Sunday.
Al-Emadi was set to remain in the Strip for two days. During that time, he will meet with Hamas officials and also take part personally in the distribution of funds to Gaza residents.
Of the funds transferred to Gaza, $10 million will be allocated to Gazan families, with each receiving $100, the other $5 million will go to the UN-funded program "Cash for Work."