* Flare-up follows killing of 2 Hamas militants
* Cairo trying to mediate truce
* Netanyahu convenes Israeli security council
* Violence up before Ramadan, Independence Day, Eurovision (Adds Palestinian baby killed, comments from Hamas, Islamic Jihad and Israeli military)
By Nidal al-Mughrabi and Maayan Lubell
GAZA/JERUSALEM, May 4 (Reuters) - Gaza militants fired dozens of rockets into Israel on Saturday, drawing a wave of Israeli air strikes that killed a Palestinian baby and a gunman, as hostilities flared across the border for a second day.
The escalation began on Friday when a sniper from the Palestinian Islamic Jihad militant group fired at Israeli troops across the border wounding two of them, according to the Israeli military. A retaliatory Israeli air strike then killed two militants from the Islamist Hamas group that rules Gaza.
Two other Palestinians protesting near the frontier were also killed by Israeli forces.
On Saturday, Hamas and Islamic Jihad fired more than 200 rockets toward Israeli cities and villages. In response, the Israeli military said its tanks and aircraft carried out attacks against more than 30 militant targets belonging to both groups.
Explosions in Gaza City, where busy streets were packed with shoppers making preparations for the holy Muslim month of Ramadan, shook buildings and sent people fleeing for cover.
The Gaza Health Ministry said a 14-month old baby was killed by one of the Israeli strikes and at least 13 other Palestinians were wounded throughout Saturday. Residents identified two of them as militants.
"The Israeli plane fired a missile near the house and the shrapnel entered the house and hit the poor baby," said her aunt, Ibtessam Abu Arar. An Israeli military spokeswoman made no immediate comment.
A small armed pro-Hamas group in Gaza, The Protectors of Al-Aqsa, said one of its men was killed in another air strike.
Across the border, sirens sent Israelis running to shelters as the blasts of rocket interceptions sounded overhead. The Magen David Adom ambulance service said two people were wounded by shrapnel.
Israeli military spokesman Lieutenant-Colonel Jonathan Conricus said Israel was prepared to intensify its attacks. He added that Islamic Jihad was trying to destabilize the border and blamed Hamas for failing to rein it in.
In a joint statement in which they claimed responsibility for firing rockets, Hamas and Islamic Jihad said: "Our response will be broader and more painful if the enemy pursues its aggression."
Although Israeli air strikes in retaliation for rockets from Gaza are a frequent occurrence, Israel and Hamas have managed to avert all-out war for the past five years.
Egyptian mediators, credited with brokering ceasefires in previous rounds of violence, were working to prevent any further escalation of hostilities.
"Egypt has stepped up its efforts with Hamas, the Islamic Jihad and Israel but there is no conclusion yet," said a Palestinian official familiar with Cairo's mediation efforts.
The flare-up, which prompted Israeli Prime Minister Benjamin Netanyahu to convene security chiefs, comes days before Muslims begin Ramadan and Israelis celebrate Independence Day.
Israel is also due to host the 2019 Eurovision song contest finals in less than two weeks in Tel Aviv, towards which long-range rockets were launched in mid-March.
The Islamic Jihad said in a statement that the rocket barrages were a response to Friday's events and that Israel has been delaying the implementation of previous understandings brokered by Cairo.
Hamas said on Thursday that its Gaza chief, Yeyha Sinwar, had travelled to Cairo for talks on efforts to maintain calm along the border and alleviate hardship in the enclave.
Some 2 million Palestinians live in Gaza, whose economy has suffered years of blockades as well as recent foreign aid cuts. Unemployment stands at 52 percent, according to the World Bank, and poverty is rampant.
Israel says its blockade is necessary to stop weapons reaching Hamas, with which it has fought three wars since the group seized control of Gaza in 2007.
Over the past few weeks, Cairo's mediation had helped persuade Israel to lift some restrictions on the movement of goods and people in and out of Gaza and expand the Mediterranean zone where Gazans can fish.
But Israel scaled back the fishing zone this week in response to rocket fire and shut the border crossings entirely on Saturday after barrages from Gaza. (Writing by Maayan Lubell; Editing by John Stonestreet and Ros Russell)
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