Then, on Wednesday, Israeli forces swept through three Gaza towns in a hunt for rockets and the militants who manufactured them.
In one incident, a local Hamas leader was shot dead in the southern Gaza town of Khan Yunis.
The attack followed an Israeli incursion into three Gaza towns.
Security installations at the Gaza town of Khan Yunes were handed over in the night, the army said.
Israeli armored vehicles also entered the southern Gaza town of Rafah in search of suspected tunnels used for weapons smuggling.
Many came from West Bank and Gaza towns that are as little as an hour away by road, but a world away culturally.
In the southern Gaza town of Rafah on Thursday, Israeli soldiers shot and killed a 16-year-old Palestinian.
Abbas made the statement shortly after three Palestinian teenage boys were shot dead by Israeli troops in the southern Gaza town of Rafah.
In addition, curfews were imposed on most Gaza towns and refugee camps, confining hundreds of thousands of people to their homes for nearly the entire week.
It is a matter of days, perhaps even hours, before the point of no return is reached with a land offensive, particularly in Gaza town.