JERUSALEM, Sept 30 (Reuters) - Israeli forces killed a Palestinian gunman in the occupied West Bank on Thursday and a Palestinian woman who tried to stab officers in Jerusalem"s Old City, Israeli police said. Hours later, in the Gaza Strip, Israeli soldiers fired towards a Palestinian, one of three people who raised suspicions by approaching Israel"s border fence, after he was spotted carrying a bag and digging, the Israeli military said. The Hamas militant group, which rules the enclave, said the man was killed, "shot by the enemy while practising his hobby of hunting". The military said it was investigating the incident, in a volatile border area where Israel maintains tight security. The violence came amid tensions heightened by the deaths on Sunday of five Palestinians, at least four of them claimed as members by Hamas, in gun battles with Israeli forces carrying out arrest raids in the West Bank. Police said in a statement Israeli soldiers and paramilitary police on an operation near the West Bank city of Jenin shot and killed a Palestinian who fired at them. A Palestinian medical source confirmed the death of a 22-year-old man. The Islamic Jihad militant group issued a statement saying he was one of its members and that he was killed in a shootout with Israeli forces carrying out a raid. In Jerusalem"s Old City, Israeli police officers shot dead a Palestinian woman who tried to stab them, police said, identifying her as a resident of the West Bank. Israel captured the Gaza Strip, the West Bank and East Jerusalem, including its Old City, in the 1967 Middle East war. It withdrew troops and settlers from Gaza in 2005. Palestinians seek to establish a state in the West Bank and Gaza, with East Jerusalem as its capital.