The two men killed in northern Beit Lahiya were Hamas snipers taking part in a live-fire exercise within a compound on Gazan territory, the group's armed wing said in a statement.
However, earlier in the evening, at least two Israelis were injured as a result of rockets that landed in Sderot.
Earlier on Wednesday, Hamas terrorists fired at an engineering vehicle near the northern Gaza Strip that was involved in the construction of a barrier along the security fence.
The violence came after two fighters from the military wing of Hamas, which governs Gaza, were killed by Israeli fire on Tuesday.
Air raid sirens sounded nearly nonstop in southern Israel from sundown on Wednesday, warning residents to stay in shelters as more than 80 rockets were fired in their direction.
"I am deeply alarmed by the recent escalation of violence between Gaza and Israel, and particularly by today's multiple rockets fired towards communities in southern Israel", said U.N. Middle East envoy Nickolay Mladenov.
NCAA announces sweeping reforms for college basketball | Lexington Herald Leader
All player-agent relationships, however, must be in writing, disclosed to the NCAA and ended when the player comes back to school. Athletes will be allowed more college-paid visits, which can begin as soon as August 1 the summer before their junior year.
Smoke plumes could be seen rising from Gaza City Wednesday evening.
"Hamas hit the "enemy" with a large number of rockets", it said.
TRT World's Mohammad Mansour reports from Gaza.
United Nations officials have however called for the blockade to be lifted, citing deteriorating humanitarian conditions in the Palestinian enclave run by Islamist movement Hamas where 80 percent of the two million population are dependent on aid.
Those killed in the Gaza Strip included Enas Khammash, 23, and her 18-month-old daughter Bayan, according to the health ministry in the Hamas-controlled enclave.
A Hamas militant was also killed in one of the strikes, while at least 12 people in Gaza were reportedly injured, health officials said.
Israel reveals 'impenetrable' sea barrier on Gaza coast
The Israel Defense Forces confirmed in a statement that an aircraft fired at the group in the northern Gaza Strip. Hamas has acknowledged that dozens of those killed were its members.
The push for a long-term ceasefire agreement follows months of clashes between Israel and Hamas, marked by a surge in cross-border arson attacks, rocket fire, and violent clashes which brought the sides to the brink of a full-scale war in two separate military flare-ups in July.
Israel says it holds Hamas responsible for all fire coming from the long-blockaded coastal territory.
The exchange came amid continued attempts by Egypt to broker a broad cease-fire deal between Israel and Hamas.
Later, Palestinians fired about 70 rockets across the border, and Israeli aircraft struck at least a dozen militant targets.
An Israeli minister said his government has rejected an European Union plan to link the Gaza Strip with the West Bank, according to Israeli media on Wednesday.
The protests call for Palestinians to be able to return to the land they or their families fled or were expelled from in the 1948 war that established the state of Israel.
Low mortgage rates not impressing potential new home buyers
One of the problems is that once rates reach rock bottom (which is pretty well where they are right now) the only way is up. This could be a good time for more young Americans to take out a Roth Individual Retirement Account or IRA for short.