A new rebel alliance said Sunday it had launched an offensive to “liberate” Syria’s largest city, Aleppo, while government troops backed by helicopter gunships wrested back control of rebel-held neighborhoods in the capital Damascus.

The attack on Aleppo, Syria’s commercial hub that has been a bedrock of support for President Bashar Assad, was a sign of the rebels’ growing confidence and capabilities days after they killed four members of Assad’s inner circle in a Damascus bombing.

“Right now, Assad’s inner circle has been dismantled and Assad has lost his balance,” Brig. Gen. Abdul Kareem Al-Ahmad of the rebel Free Syrian Army said at a meeting in Turkey. “This war is now being waged in the heart of Syria in Damascus.”

The killing of senior regime figures, a series of high-level military defections, and the capture of several border crossings have given the rebel side unmistakable momentum over the past week and put the regime on the defensive. After struggling for nearly a week to put down a rebel challenge inside the capital, regime forces appeared close to regaining control of Damascus.

The battles in Damascus and Aleppo signal a new and bloody phase of Syria’s civil war, with combat in heavily populated cities.

With the conflict moving from the countryside and smaller cities into the two main urban centers, an activist group said the death toll had risen to more than 19,000 since the uprising began in March 2011. The Syrian Observatory for Human Rights also said July is shaping up to be the deadliest month of the conflict so far, with 2,752 people killed in the first three weeks — already nearly as many as the previous month.

The escalating bloodshed and increasing chaos is threatening to spill across borders into a larger regional conflagration. It has put Syria’s neighbors, particularly Israel, on edge.

Israeli Prime Minister Benjamin Netanyahu said in an interview with Fox TV that his “principle concern” is the political chaos that might ensue if Assad falls and the Syrian- and Iranian-backed Lebanese militant group Hezbollah gains access to Syria’s stockpile of chemical weapons, rockets and missiles.

He said Israel hasn’t considered specifically trying to cross the border and seize the weapons.

“There are other possibilities,” he said without elaborating. “We’ll have to consider our actions. ... Do I seek action? No. Do I preclude action? No.”

There have been no indications that Shiite Hezbollah is active in Syria, where the rebels are largely Sunni.

King Abdullah of Saudi Arabia, a Sunni power and major regional rival of Iran, has announced the start of a “national campaign to collect donations to support our brothers in Syria.” That suggested the oil-rich kingdom may be looking to boost its financial support for the rebels, which they are already believed to be funding.

The opposition has taken control of several border crossings with Iraq and Turkey over the past few days. A video posted online by activists Sunday showed about a dozen gunmen standing in front of the newly captured Bab Al-Salamah crossing on the Turkish frontier as they raised the Syrian opposition flag. It is the second Turkish crossing captured in a week.

Yet, even as the rebels seized one crossing, they abandoned another. Iraqi military officials and state television reported that Syrian government forces retook control of the Rabiya crossing in the north after rebels pulled out. Far to the south, the rumble of fighting could be heard from the larger Bukamal crossing near the Iraqi town of Al-Qaim in the desert. The rebels took control of Bukamal on Thursday.

Brig. Gen. Manaa Rahal of the Free Syrian Army trumpeted the seizures of the Turkish border crossings as key to the rebel struggle.

“The seizure of these border crossings was a crucial victory for the opposition and its strategic importance will only increase,” he said in the meeting in Turkey’s Hatay province.

Damascus and Aleppo, the country’s largest cities with populations of 2.5 million and 3 million respectively, are both home to elites who have benefited from close ties to Assad’s regime, as well as merchant classes and minority groups who worry their status will suffer if Assad falls.

Col. Abdul-Jabbar Mohammed Aqidi, the commander of what appeared to be a new confederation of rebel groups called the Unity Brigade, said in the video posted on Youtube: “We gave the orders for the march into Aleppo with the aim of liberating it.”

He called on government troops to defect and join the opposition, and said rebels will protect members of Assad’s Alawite minority sect, an off-shoot of Shiite Islam, saying “our war is not with you but with the Assad family.”

The Britain-based Syrian Observatory for Human Rights and Aleppo-based activist Mohammed Saeed said the fighting is concentrated in several neighborhoods. He said rebels are in full control of the central Salaheddine district and the nearby Sakhour area. He added that thousands of residents have fled tense quarters of the city for safer neighborhoods and the suburbs.

“Aleppo is witnessing serious street battles,” Saeed said, with fierce clashes on the road leading to the city’s international airport, known as Nairab, as rebels tried to surround the airfield to prevent the regime from sending reinforcements.

Syrian state TV, however, played down the scale of the violence, saying government troops were hunting down “terrorists” and killing large numbers of them. The government refers to those trying to overthrow Assad’s regime as “terrorists.”

In Damascus, the Observatory also reported attacks by government forces in the neighborhoods of Mazzeh and Barzeh that had once been held by rebels. It said that troops used helicopters gunships in the attack, causing heavy casualties.

Maj. Gen. Nabil Zughaib, described as a missile expert, was also shot dead along with his wife and a son in the Damascus neighborhood of Bab Touma, according to the Observatory.

Syrian state TV denied government forces were using helicopters in Damascus, and said the capital was calm and troops were just mopping up the remnants of the “terrorists” in cooperation with residents.

Television also showed images of calm streets in Damascus and workmen cleaning up rubble in the once-rebel held Midan neighborhood, in effort to portray a capital where everything has returned to normal.

Assad appeared on state TV receiving Gen. Ali Ayyoub, the new army chief of staff, whose predecessor replaced the defense minister slain in the bombing. It was only Assad’s second appearance since the attack.

Despite the regime’s efforts to present an image of calm in the capital, Malaysia’s government said it was shuttering its embassy in Damascus and evacuating more than 130 students and diplomats, while Italy ordered of its citizens to leave the country because of the “progressive deterioration” of the situation.