The appeal was filed by an Israeli NGO, We Are Refugees, in a petition against Defence Minister Ehud Barak and Interior Minister Eli Yishai for refusing to allow the group of Eritreans, who are seeking political asylum, into the country.
Since last Thursday, the Eritreans -- hoping to apply for political asylum -- have been stuck in an area between the Egyptian and Israeli border fences, which is technically within the sovereign borders of the state of Israel, the NGO said.
The group reportedly includes men, women and a 14-year-old boy.
In the Thursday court session, the state argued that Israel "could decide who to let into its borders," and that refugees who reach Israel via Egypt should receive that status from Egypt.
In a statement following the hearing, the court announced it would hold a further session on Sunday.
The court also noted that "we heard from the (state) representatives that the people who are the subject of the petition are receiving food and water, and will receive medical treatment if the need arises."
But Physicians for Human Rights-Israel, which sent a medical delegation to the border on Thursday, cited an officer at the site as saying water was being supplied but the army "had not provided food to the refugees."
An update on the NGO's Facebook page said their doctors and a nurse who wished to examine the Eritreans were refused access.
Media reports quoting soldiers stationed at the site say the Eritreans have not eaten in a week and have been given only a limited supply of water.
"Israel's refusal to provide them with food, medical treatment, and to hear their asylum request is a clear violation of the 1951 UN Refugee Convention, which Jewish organisations helped draft in the aftermath of World War II, and Israel was the fourth country to ratify," the NGO said.
Citing information provided by soldiers, it said the minor was "in serious condition, that a pregnant woman miscarried and that the group has not received food since last Thursday."
Israel on Wednesday denied it had any legal obligation to let them in.
"The attorney general ruled today that there is no legal obligation to take in anyone located beyond the border," said the interior ministry.
"According to international practices and binding precedents, the fence is a de facto border, and therefore anyone who is beyond it is not located in Israeli territory and is therefore not eligible for automatic entry," a government spokesman said on condition of anonymity.
"There has been no determination by any international body according to which Sudanese or Eritrean citizens are persecuted in Egypt or that their lives are in danger.
"Therefore, there is no legal obligation to allow entry into Israel of those who are near the fence."
Israeli figures indicate there are already around 60,000 Africans living illegally in the country, most of them from Sudan and Eritrea.
Israel earlier this year launched a major campaign to round up and deport illegal African migrants, sparking an outcry from rights groups.