Sirens wailed across Israel's main metropolis moments before an explosion was heard, but police said the rocket appeared to have fallen into the sea.
Israel said it halted its incessant air attacks on militant targets in Gaza during the brief visit of Egyptian Prime Minister Hesham Kandil, though Hamas security claimed three airstrikes hit the territory during that period. Militants, meanwhile, fired off more than 60 rockets after Kandil arrived in Gaza.
Kandil toured Gaza City's Shifa Hospital, accompanied by the territory's prime minister, Ismail Haniyeh of Hamas, who was making his first public appearance since Israel's offensive began Wednesday.
In one chaotic moment, a man rushed toward the two leaders, shouting as he held up the body of a 4-year-old boy. The two men cradled the lifeless boy who Hamas said was killed in an Israeli airstrike - a claim Israel denied.
Fighting to hold back tears, Kandil told reporters that the Israeli operation must end.
"What I saw today in the hospital, the wounded and the martyrs, the boy ... whose blood is still on my hands and clothes, is something that we cannot keep silent about," he said.
Israel vociferously denied carrying out any form of attack in the area since the previous night. The pace of cross-border fighting quickly resumed after the Egyptian leader's departure.
The violence has widened the instability gripping the region, straining already frayed Israel-Egypt relations. The Islamist government in Cairo, like Hamas linked to the region-wide Muslim Brotherhood, recalled its ambassador in protest and dispatched Kandil to show solidarity with Gaza.
Israel, meanwhile, signaled a ground invasion might be imminent, with troops, tanks and armored personnel carriers massing near the Palestinian territory.
The Israeli military "continues to strike hard against Hamas and is prepared to expand its action into Gaza," Israeli Prime Minister Benjamin Netanyahu said.
The operation began with the assassination of Hamas' military chief and dozens of airstrikes on rocket launching sites. While Israel claims to have inflicted heavy damage, militants have fired hundreds of rockets into southern Israel, bringing the entire region to a standstill.
At least 22 Palestinians, including 12 militants and six children, as well as three Israelis have been killed in three days of fierce fighting.
The 4-year-old boy whose body had been handed to Kandil and Haniyeh was killed along with a young man earlier Friday when an Israeli missile struck close to their homes in the town of Jebaliya near Gaza City, relatives said.
The area near the boy's home showed signs that a projectile had exploded there, with shrapnel marks in the walls of surrounding homes and shattered kitchen windows. But neighbors said security officials quickly took what remained of the projectile, making it impossible to verify who fired it.
Kandil's visit came after a night of fierce exchanges. Overnight, the military said it targeted about 150 rocket-launching sites as well as ammunition warehouses, bringing to 450 the number of sites struck in the three-day operation.
Militants unleashed dozens of rocket barrages overnight, setting off air-raid sirens throughout an area that is home to some 1 million Israelis.
Fighting between the two sides escalated sharply Thursday with a first-ever rocket attack from Gaza on the Tel Aviv area, menacing Israel's most densely populated area. For the attack, they unleashed for the first time the most powerful weapons in their arsenal - Iranian-made Fajr-5 rockets.
No casualties were reported there, but three people died in the country's rocket-scarred south when a projectile slammed into an apartment building.
Early Friday, 85 missiles exploded within 45 minutes in Gaza City, sending black pillars of smoke towering above the coastal strip's largest city. The military said it was targeting underground rocket-launching sites.
One missile flattened sections of the Interior Ministry, leaving a huge pile of rubble. Another hit an uninhabited house belonging to a senior Hamas commander. Those strikes, together with an attack on a generator building near Haniyeh's home, suggested that Israel was expanding its offensive beyond military targets.
Ten-month-old Haneen Tafesh was killed Thursday when flying shrapnel from an air attack on a field next to her family's shack struck her in the head.
"What did she do? Did she fire any rockets?" her 23-year-old father, Khaled Tafesh, asked as he waited outside the Shifa hospital morgue, waiting for the funeral of his only child to begin.
Israel and Hamas had largely observed an informal truce since a devastating Israeli incursion into Gaza four years ago, but rocket fire and Israeli airstrikes on militant operations continued sporadically.
The Israeli offensive has not deterred the militants from firing more than 400 rockets aimed at southern Israel, the military said.
The rocket attacks aimed at Tel Aviv raised the likelihood of a ground incursion. After the two rockets struck close to the city on Thursday, the government approved the mobilization of up to 30,000 reservists.
Those rockets also appear to have landed in the Mediterranean Sea, defense officials said, and another hit an open area on Tel Aviv's southern outskirts. No injuries were reported.
An Israeli ground offensive could be costly to both sides. In the last Gaza war, Israel devastated parts of the territory, setting back Hamas' fighting capabilities but also paying the price of increasing diplomatic isolation because of a civilian death toll numbering in the hundreds.
In the current round of fighting, the civilian casualties have been relatively low and the Israeli strikes seem to be more surgical.
(Copyright 2012 by The Associated Press. All Rights Reserved.)