JERUSALEM — A surge in violence on Wednesday across the Israel-Gaza border prompted strong warnings from Israeli leaders that if pushed, Israel would act more forcefully against militants in Gaza, the Palestinian coastal enclave.

Palestinian militants fired more than 60 rockets from Gaza into southern Israel overnight and early Wednesday, hitting several houses and wounding three Thai workers, two critically, in an Israeli border community, according to the Israeli military. Israel carried out several airstrikes against rocket-launching squads, killing four militants, Palestinian officials said. Three of the four belonged to Hamas, the Islamic militant group that controls Gaza.

The rocket fire began hours after a landmark visit to Gaza by the emir of Qatar, Sheik Hamad bin Khalifa al-Thani, the first head of state to visit Gaza since Hamas took full control there in 2007. It also came as a major American-Israeli joint military exercise was under way in Israel, underlining the volatility in the area at a delicate time before the American elections, in less than two weeks, and Israeli elections, scheduled for January.

The Israeli government has come under increasing criticism from residents of southern Israel who have been forced into protected spaces and bomb shelters during repeated bouts of cross-border violence.