Undeterred by a wave of casualties, Syrian rebels say they will not back down in their quest to seize Aleppo, the country's commercial hub and its second-largest city.

After six days of fighting, the battle with government forces raged again Thursday as helicopter gunships flew over the city, the opposition Syrian Observatory for Human Rights said. At least one rebel fighter was killed, the group said.

"They don't seem to have the kind of weapons necessary," New Yorker reporter Jon Lee Anderson told CNNI's "Amanpour" from Aleppo about the rebels who, he said, believe the battle to be a decisive one.

"If Bashar al-Assad can't dislodge them from Aleppo, then it's over for him. So they have to fight to the death."

A rebel commander north of Aleppo told CNN he was sending 300 more fighters to bolster forces in Aleppo. The commander said the rebels were on the offensive in Aleppo, where 18 of 22 rebel brigades were located.

In preparation for a fresh onslaught expected after Friday prayers, rebels were setting up medical clinics in apartments and homes throughout the city, he said.

The seat of al-Assad's power also saw renewed violence Thursday as explosions rocked Damascus, another opposition group said.

Regime forces battled rebels in several Damascus neighborhoods, and the Palestinian refugee camp of Yarmouk came under "fierce helicopter shelling with machine guns," the Local Coordination Committees of Syria said.

The LCC reported dozens of dead and wounded in shelling by regime forces in the capital city's suburb of Yalda, and in bomb attacks in the Mashtal district of Damascus.

The death toll for Thursday across Syria reached 200, including a number of children, women and defectors, the LCC said.

Forty-eight died in Aleppo, 46 in Damascus and its suburbs; 30 in Daraa; 27 in Idlib; 21 in Homs; 14 in Deir Ezzor; six in Hama; four in Raqqa, two in Latakia, one in Qunaitera and one in Hasaka, it said.

The LCC said Thursday marks the first time since the start of the uprising in March 2011 that Aleppo has led in the number of deaths in a single day across Syria.

Some of those killed in the Al-A'ajamy Valley were defected soldiers seeking "to save civilians fleeing from shelling," the group said.

Video posted on YouTube appears to show youths demonstrating in the central Damascus neighborhood of Qanawat.

"The people united, will never be divided," they chant in English. "The Syrians united, will never be defeated."

And, "Hey Bashar, damn your soul. Hey Bashar, damn your soul."

Rebel militias are composed largely of soldiers who have defected from the Syrian military. But there are also many civilians -- including students, shopkeepers, real-estate agents and even members of the president's ruling Ba'ath party -- all trying to end four decades of al-Assad family rule.

A Sunni cleric in the village of Injara, about six miles west of Aleppo, showed CNN craters and gaping holes in at least six homes, the result of what he and other residents said were rockets and artillery from a Syrian army base a couple of miles away.

"They hit us every night," Sheikh Ali Bukhro said.

Other residents said they had had neither electricity nor running water in more than a month. Some men said they had sent their families to refugee camps in Turkey, where more than 40,000 Syrian refugees have taken shelter.

In Washington, State Department spokeswoman Victoria Nuland said U.S. officials had "grave concerns" about the situation in and around Aleppo and Damascus.

"This is the concern: That we will see a massacre in Aleppo -- and that's what the regime appears to be lining up for," she told reporters.

Given that China and Russia have vetoed attempts by the Security Council to act, "we have to double our efforts with like-minded nations outside of the U.N. system," she said.

"This is a horrific situation, this is abhorrent what this regime is willing to do against its own people. We have to call it out, we have to do what we can to strengthen the opposition for the day after. We have to do what we can in coordination with others in the international community."

The British ambassador to the United Nations said reports of warplanes over Aleppo were especially concerning.