A new round of violence between Israel and Gaza militants continued Wednesday morning.

A Grad rocket exploded near the Israeli city of Beersheba and another ten landed in open areas near communities in the western Negev. There were no reports of casualties or damage.

More than 50 rockets and mortar shells were fired towards Israel on Tuesday, 22 of which landed in the western Negev, according to local media reports.

Later in the evening, an Israeli Border Police officer sustained moderate injuries and three other officers were slightly wounded from shrapnel, as they were searching for remains of fallen projectiles.

While on the Palestinian side, a Palestinian militant was killed Wednesday in a fresh Israeli airstrike in the southern Gaza Strip town of Rafah, witnesses and medical sources said.

So far, seven Palestinians have been killed since Monday by Israeli fire. On Tuesday, a Palestinian rocket fell short of the borders and killed a toddler in Gaza City.

Hamas' military wing, the Izadeen al-Kassam Brigades, claimed responsibility for launching rockets since hostilities broke out on Monday, and said the attacks were a response to the killings of Palestinians in recent days.

Israeli officials said the attacks were highly unusual for Hamas, which has refrained from lobbing rockets over the past year. Instead, the organization gave other groups the go-ahead to fire into Israel.

Israel said it was not seeking an escalation, but Defense Minister Ehud Barak convened top security and intelligence officials for consultations late Tuesday night to review options of response.

Israeli Vice Prime Minister Silvan Shalom on Tuesday warned that "the more things deteriorate, the closer we come to a decision we don't want to make."

"The prospect of a ground operation (in Gaza) shouldn't frighten us," Shalom told Israel Radio.

Meanwhile, the ongoing rocket fire has forced thousands of Israelis to seek cover in neighborhood bomb shelters and reinforced rooms in homes.