NORTHERN SYRIA (CNN) -- 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 a crucial city in the Syrian civil war.

After six days of fighting, the seesaw 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.

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

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

In the past week, the civil war has pushed into Syria's two largest cities, Aleppo and Damascus.

On Wednesday, opposition fighters burned a police station and captured pro-regime forces, rebels said.

Rebel militias are largely composed of soldiers who 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 residents said were rockets and artillery from a Syrian army base visible a couple of miles away.

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

Other residents lamented that they have not had electricity or 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.

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

"The reports now of attacks by regime fighter jets in Aleppo mark yet a further dangerous escalation and underlines that there are no boundaries that the Assad regime will not cross in the misguided hope that it can resist the will of its people and hang on to power," British Ambassador Mark Lyall Grant told the U.N. Security Council on Wednesday.

The front page of Syrian pro-regime newspaper al Watan carried the headline "Aleppo... the Mother of all Battles" on Thursday.

At least 31 people were killed across Syria on Thursday, according to the LCC, among them 14 in Aleppo and seven in Damascus and its suburbs.

A day earlier, at least 129 were killed, including 22 in Aleppo and 27 in and around Damascus, the LCC said.

Speaking Thursday at a memorial to those who died in the Srebrenica massacre in the Balkans in the 1990s, U.N. Secretary-General Ban Ki-moon urged the Syrian government and the opposition forces to cooperate with the United Nations in bringing the conflict to an end.

The U.N observer mission in Syria has not been able fully to do its job "because of the noncompliance of the parties -- the government parties and also opposition forces," he said.

The six-point peace plan brokered with U.N. special envoy to Syria Kofi Annan and U.N. Security Council resolutions must also be implemented "without further delay," he said.

"At this time again I am urging all the parties: They must stop fighting and killing people now. They have to begin political dialogue for a political resolution of this crisis," Ban said.

After 16 months of chaos, more officials from al-Assad's regime have resigned.

The opposition Syrian National Council said Wednesday that two senior Syrian diplomats were the latest to defect.

One is the Syrian ambassador to the United Arab Emirates, Abdullatif Al Dabbagh, SNC spokesman George Sabra said.

The second is Al Dabbagh's wife, Lamia Al Harriri, who is a Syrian envoy to Cyprus. She defected to Qatar, SNC member Najy Tayyarah said. Al Harriri is also the niece of Syrian Vice President Farouq Al Sharea.

But on Thursday, a Syrian official downplayed the reports of recent defections.

Syrian Foreign Ministry spokesman Jihad Makdissi said Dabbagh "was called to Damascus for consultations with the minister and has been off duty ... since June 4."

In addition, Makdissi said, Al Harriri has never been a Syrian ambassador. "She is a diplomat who was tasked with managing affairs on behalf of the embassy charge d'affaires pending the appointment of an ambassador."

The Syrian crisis started in March 2011, when a fierce government crackdown on peaceful protesters morphed into a nationwide uprising against the regime.

The LCC says more than 16,000 people have been killed in the conflict. The U.N. secretary-general said this week that almost 17,000 people have died.

CNN's Ivan Watson reported from northern Syria; Holly Yan reported from Atlanta. CNN's Salma Abdelaziz, Yousef Rafayah and Richard Roth also contributed to this report.