Palestinian security sources said a senior Islamic Jihad movement commander and a gunman belonging to the group were killed early on Tuesday morning in an exchange of fire with Israeli forces.
An Israeli military spokesman only confirmed the death of the commander, who was allegedly preparing an attack on Israel.
The six-month truce between Israel and Hamas-led militants, which came into force at 06:00 a.m. local time (03:00 GMT) on June 19, is limited to the Gaza Strip, and does not cover the West Bank. The terms of the Gaza ceasefire have been strictly adhered to by both sides since Thursday. However, the deaths of the Palestinian militants in the West Bank may test the strength of the truce.
Under the agreement, Israel will gradually abolish economic sanctions imposed on Gaza, and the sides will continue to negotiate the release of the kidnapped Israeli soldier Gilad Shalit, who has been held captive in Gaza for almost two years.
Israeli Prime Minister Ehud Olmert last week described the ceasefire as "fragile" and said he expected it to be "very short."