Benghazi, Libya (CNN) -- Eyewitnesses in the embattled Libyan city of Misrata reported especially intense shelling by Moammar Gadhafi's forces overnight -- the heavy fire picking up at about the same time reports came out that one of the leader's son was killed in a NATO airstrike.
"There's been continuous and heavy shelling for three hours straight," said one man, talking to CNN from about three miles from Misrata's city center Sunday. "There have been a lot of explosions."
Heavy gun and artillery fire could also be heard early Sunday throughout Benghazi, which is the hub for rebel forces and their transitional government.
The eyewitness in Misrata, the country's third-largest city, speculated that the intensified attacks were tied directly to reports that Saif al-Arab Gadhafi, the sixth of Moammar's eight children, died in an attack on his Tripoli home. He said there was significant damage and some casualties, though there were only rebel forces and none aligned with Gadhafi in the city itself.
Government spokesman Musa Ibrahim said that several of the Libyan leader's grandchildren also died in the attack, though Moammar Gadhafi and his wife -- both of whom were in the residence when it was hit -- are unhurt.
"It's going to be like revenge," said the witness in Misrata, who supports the opposition, of the intensified attacks.
These stepped-up, continuous attacks were reported early Sunday, about a full day after Moammar Gadhafi's latest diatribe that called for a negotiated end to NATO airstrikes and included threats to Italy.
During his rambling 45-minute speech, he urged NATO to negotiate an end to airstrikes, accusing the international coalition of killing civilians and destroying the nation's infrastructure in a bid to take over its oil production.
"Come and negotiate with us. You are the ones attacking us. You are the ones terrifying our kids and destroying our infrastructure. You American, French and British come and negotiate with us," Gadhafi said on Libyan state TV.
The Libyan leader remained defiant, as he sharply criticized those behind the attacks and questioned their intent.
"What are you trying to do? Trying to take the oil?" he said. "The Libyan people will not allow you ... The oil is under control of the Libyan government and for the people."
He called on the United Nations to review the NATO attacks, saying his country agreed to a cease-fire.
"We are the first ones who wanted and agreed on a cease-fire. But the NATO crusader airstrike did not cease," he said. "It cannot be a cease-fire from one side."
Hours later but before reports of Saif al-Arab Gadhafi's death, the head of NATO rebuffed the Libyan leader's comments, insisting that the mission to target his forces will continue as long as civilians remain under fire.
NATO Secretary-General Anders Fogh Rasmussen "reject(ed) any threat against Italy or any other ally," while vowing that the coalition would continue to pursue its mission.
"The Gadhafi regime continues to cause widespread suffering through its attacks on the Libyan population. Quite simply, this must stop," Rasmussen said in a statement. "NATO remains firm -- we will continue our operation until the threat to the civilian population of Libya is removed."
The airstrikes started after the U.N. Security Council approved a resolution authorizing any means necessary to protect civilians demanding the ouster of the ruler, who has been in power for nearly 42 years.
From the time NATO began its operation on March 31, the organization had conducted 4,398 sorties, of which 1,821 were strike sorties, according to an update issued Saturday. Facilities in or around Tripoli, Zintan, al-Brega and Sirte were targeted on Friday, it said.
Shortly after Gadhafi's speech, a NATO spokeswoman called for actions, not words, in expressing skepticism the Libyan leader could be trusted to follow through on his pledges.
"The regime has announced cease-fires several times before and continued attacking cities and civilians," NATO deputy spokeswoman Carmen Romero said in a statement.
"Just hours before Col. Gadhafi spoke of a truce, his forces indiscriminately shelled Misrata, killing many people, including children. His forces tried to mine the port to block the access of humanitarian aid to the beleaguered civilians of Misrata. All this has to stop, and it has to stop now."
A spokesman for the Libyan opposition accused Gadhafi of lying and trying to play both sides.
"He's playing both parts. He's buying time at the same time projecting himself as somebody who's trying to find a solution to this problem, while the reality on the ground is he is the one who's seeking to kill and carry out all kind of crimes against the Libyan people," said Jalal al Gallal.
"The man has no credibility anymore," he added.
This back-and-forth came as eyewitnesses reported difficult conditions in Misrata, amid intense shelling and blockage of any assistance.
Ibrahim said no ships can "dock at the port without being inspected by the Libyan government," saying any aid must go through designated land routes.
The Libyan governmentthreatened to sink any ship approaching the besieged port city of Misrata. The declaration essentially threatens NATO patrols and humanitarian aid ships that have been bringing in food and medical supplies, and ferrying out refugees and the wounded.
This threat came shortly after NATO said it intercepted government forces laying mines in Misrata's harbor, which has been a lifeline for humanitarian aid.
At least nine people were killed and 30 more wounded in Friday's attacks in Misrata, said a doctor, who is a member of the medical committee in the city.
"There is an indiscriminate shelling now in Misrata," said the doctor, who asked not to be identified because he feared retribution by Gadhafi's forces.
CNN's Greg Botelho, Frederik Pleitgen, Kareem Khadder and Saad Abedine contributed to this report.