Abbas' comments were made in a televised address ahead of Palestinian Prisoners' Day on Sunday.
The Palestinian Authority said around 6,000 Palestinians were currently in prison inside Israel and that Israel had detained over 70,000 Palestinians over the last decade.
Twelve Palestinian lawmakers are in jail in Israel, the government said in a statement.
UN Humanitarian Coordinator Maxwell Gaylard expressed concern over the treatment of Palestinian detainees and insisted that "the rule of law must be applied to all of the approximately 6,000 Palestinian prisoners in Israeli detention, in line with international human rights and humanitarian law," in a statement from his office.
"Israel's policies and practices regarding Palestinian prisoners raise a number of concerns, including a lack of clarity on the legal status of such prisoners, the location and conditions of their incarceration, the need for access to legal counsel and representation, the issue of administrative detention, and the prevention of family visits for detainees from Gaza," the statement said.
Gaylard noted that the practice of detaining Palestinians in Israel was contrary to the Geneva Conventions, and he expressed particular concern for the plight of Palestinian women and children detained in Israel.
The PA said Israel had "systematically violated the most basic rights granted by international and human rights conventions through inhumane treatment, restrictions on movements, killings, deportation, and detention," since Israel occupied the West Bank and Gaza.
Since 1967, Israel has detained more than 750,000 Palestinians, including women and children, a government statement said.
Over 200 Palestinians have died in Israel prisons. Of these, 74 were murdered, 70 died after being tortured and seven were shot dead by prison guards, the PA said.
The longest-serving political prisoner in the world was Palestinian, the PA said. Nael Al-Barghouti has been detained in Israel for 33 years. His brother, Fakhri, is also in an Israeli prison.
Fatah Youth called on the international community to protest Israel's violations of international law, particularly its imprisonment of Palestinian children, the long-term detention of Palestinians without charge or trial, the physical and psychological torture of political prisoners and the refusal to allow Gaza residents to visit their detained relatives.
In a statement, the youth movement noted that since 1967, around 40 percent of Palestinian men living in the occupied territories had been detained by Israel.
