The officials spoke on condition of anonymity because they were not authorised to brief the media.
In 2007, Hamas wrested control of Gaza by force, provoking the Israeli-Egyptian blockade that severely restricted the movement of most of Gaza's 2 million inhabitants.
The Rafah crossing is Gaza's main gate to the outside world but has only had sporadic openings since the 2013 ouster of Egypt's elected Islamist President Mohammed Morsi, a high-ranking member of Hamas' parent group, the Muslim Brotherhood.
Meanwhile, United Nations human rights chief Zeid Ra'ad al-Hussein said yesterday that Israel has systematically deprived Palestinians of their human rights, with the residents of Gaza "caged in a toxic slum from birth to death".
Opening a special session of the UN Human Rights Council that could set up a commission of inquiry into recent violence, Zeid said: "Nobody has been made safer by the horrific events of the past week. End the occupation, and the violence and insecurity will largely disappear."
- AP