There was a second day of violence, Wednesday, on the border between Israel and the Gaza Strip.
Israel says it will do whatever it takes to halt rocket and mortar attacks, and did not rule out a ground attack.
For its part, Israel has carried out air strikes, killing at least four men it says were militants.
Israel is also criticizing a visit to Gaza by the Emir of Qatar, a US ally.
It's the first visit to Gaza by a head of state since Hamas seized power in 2007.
The World's Middle East correspondent, Matthew Bell, says Qatar is seeking to gain influence and credibility with other Arab populations.
But Israel says the Emir's visit is emboldening Hamas.
"All the experts say neither Israel, not Hamas, wants to go to war," says Bell.
But things could easily slip out of control.
"If one of these rockets hits a hospital or a school," says Bell, "and kills a bunch of people, then all bets are off."