Palestinian security officials confirmed Mansur's identity as a commander in Hamas, the Islamic movement that controls Gaza.
Hamas and Fatah, which respectively control Gaza and the West Bank, have long been political rivals.
Foreign relations: Hamas, which controls Gaza, is shunned by many Arab countries and the West.
At the time Egypt controlled Gaza, only a few miles from Bethlehem.
Israeli officials say the restrictions are essential for preventing the supply of weapons to Hamas, the Palestinian militant group which controls Gaza.
Hamas, which controls Gaza and refuses to renounce violence against Israel, said the proposed peace talks would do nothing to help the Palestinian cause.
With Hamas controlling Gaza, it was not clear that Mr. Abbas had the power to carry out his decrees.
In June 1967, Israel controlled Gaza after the Six-Day War.
Using more professional tactics and clearly better motivated, Hamas fighters control northern Gaza and much of Gaza City.
The measure is part of an effort to control Gaza and to show Palestinians that they face economic punishment for the uprising, the official said.