Israeli soldiers are refusing to allow entry to a group of about 20 Eritrean refugees trapped for six days between Egyptian land and a high steel fence that Israel has erected along its southern border. Despite high temperatures and lack of shade, the soldiers have been instructed to provide only limited quantities of water.

The Israeli interior minister, Eli Yishai, said Israel "must act with a heavy hand". The country had "a very clear policy and a border fence", he told Army Radio. "We cannot let them enter."

The group, which includes two women and a child, are refusing to return to Egypt. Technically, they are on Israeli territory but the recently erected fence prevents them advancing.

According to Israeli media reports, one of the women was visibly pregnant, but migrants told the soldiers watching the group she had miscarried.

The refugees have not been offered food since arriving at the spot in the northern stretch of the Israel-Egypt border last Thursday. Temperatures in the desert area are expected to peak at about 33C on Wednesday.

In a statement, the Israeli Defence Forces said: "The area under question has a long expanse of fence that was recently built in order to prevent unauthorised infiltration into Israeli territory. On the western side of the fence, on Egypt's side, is a group of foreigners whose entrance into Israel has been prevented thanks to this fence. For humanitarian reasons, [Israeli] forces have been providing the foreigners with water."

The Association for Civil Rights in Israel condemned the refusal to allow the refugees entry. "Israel has the right to build a fence, but a fence does not relieve Israel from its obligations," said Oded Feller. "When people are standing at the fence and begging for their lives, we must make sure they are not in danger, and if they are, they must be let in."

Yishai told Army Radio: "Every day there are people stuck there. If there were no fence, and if we weren't steadfast, there would be a million people here."

He conceded that it was hard to see the pictures, but added: "I am the one who has to make the difficult decision, and if I have to choose between the good of the state, its civilians and its security, [and the good of the families] I will choose that there be a fence, that they won't enter and instead return to their country."

Last month, another group of refugees were trapped in similar circumstances for several days before they were admitted to Israel for humanitarian reasons, and taken to a detention centre.

Israel began building the fence along its 150-mile southern border last summer and it is due to be completed by the end of this year. According to the Population and Immigration Authority, the number of migrants entering Israel from Egypt fell to 200 in August, compared with 2,000 a year earlier.

An Israeli government spokesman said: "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."

No international body had determined that Eritrean or Sudanese citizens were being persecuted in Egypt or that their lives were in danger, he added. "Therefore, there is no legal obligation to allow entry into Israel of those who are near the fence."

The presence of migrants from sub-Sahara Africa in Israel has become a volatile political and social issue over recent months. A number of buildings housing African migrants have been firebombed, and some politicians have stoked anti-migrant sentiment. One described migrants from Sudan as "a cancer in our body". The prime minister, Binyamin Netanyahu, said the "flood" of migrants "threatens our existence as a Jewish and democratic state".

About 62,000 African migrants had entered Israel by May this year, according to the immigration authority. Israel's population is 7.8 million.

Human Rights Watch said on Wednesday that hundreds of migrants trying to reach Israel were being held by traffickers in Sinai; it said they were tortured, raped and sexually assaulted in an attempt to extort ransom payments from their families.

The organisation had "received numerous reports in recent years of organised criminal groups detaining asylum seekers and migrants in Sinai for extortion before allowing them to complete the journey to Israel", it said.

"The sums traffickers demanded from the migrants have increased from about $2,500 [£1,580] in 2009 to as much as $30,000 [£19,000]. The traffickers torture the migrants and beat them while they plead with relatives abroad by phone for money to meet their captors' demands. Victims include children as young as 14."