Mahmoud Zahar, a leader of the Palestinian Islamist group, made the announcement on Thursday after talks with Egyptian intelligence chief Omar Suleiman in Cairo.
Hamas had previously demanded that a truce apply simultaneously to both areas, but Israel refused.
Under the Hamas proposals, Israel would immediately cease all military activity in the Gaza Strip, and in return Hamas would halt rocket barrages at Israeli border towns, and all other militant activity.
Israel and Egypt would also permit the opening of the Rafah crossing, and ease cargo shipments into and out of the crowded Palestinian enclave.
An Israeli government spokesman said on Friday that Tel Aviv was not ready to accept Hamas's ceasefire proposal, seeing it as merely an attempt by the militants to play for time.
Israel and Egypt restricted movement of people and supplies in and out of Gaza after Hamas won the 2006 Palestinian parliamentary election, and further tightened the blockade after the group seized Gaza from President Abbas' Fatah in June, leaving the Palestinian leader in control of only the West Bank.
Israel refuses to engage in talks with Hamas, which it considers a terrorist organization.
Two Israelis were shot dead on Friday in the West Bank in an apparent militant attack, the Israeli army press service said.
The bodies of the two men were discovered at their workplace in the Netzanei Oz industrial zone near the Palestinian-ruled town of Tulkarm. No groups have claimed responsibility for the attack.
