Syrian President Bashar Assad’s troops battled rebels in the outskirts of Damascus on Wednesday and pressed on with a counteroffensive against opposition fighters in the south to prevent their advance on the capital.

The fighting came as U.S. Secretary of State John Kerry was meeting with Syrian opposition leaders in London to discuss ways to step up aid to rebels fighting to topple the regime in Damascus.

With the recent influx of better weapons and other foreign aid, the rebels have made major gains in the south, seizing military bases and towns in the strategically important region between Damascus and the border with Jordan, about 160 km from the capital.

In their campaign to topple Mr. Assad, the opposition fighters hope to eventually storm Damascus from the south.

The Britain-based Syrian Observatory for Human Rights said Wednesday’s clashes were focussed on opposition strongholds around the capital, including the suburbs of Daraya and Harasta. Fighting also raged in and around the northern city of Aleppo, Syria’s largest city and its main commercial hub, they said.

The activists said both sides sustained losses on the two battlefields. Damascus suburbs and Aleppo have been the scene of major urban warfare in Syria’s two-year uprising against Mr. Assad’s rule. The revolt started as peaceful protests inspired by other Arab Spring uprisings but later descended into civil war.

At least 28 rebels and 13 soldiers were killed in the fighting around Damascus, while 15 opposition fighters and 28 government troops died in the fighting in Aleppo on Wednesday, the Observatory said.

The group relies on a network of Syria-based activists that have been tracking the number of dead, injured and missing since the Syrian conflict began in March 2011.

The government brought reinforcements to Damascus suburbs and further south on Sunday to regain control of areas the rebels recently captured between the Jordanian border and Damascus, the seat of Mr. Assad’s power.

Both sides consider Damascus the ultimate prize in the civil war.

The rebels now control large swaths of northern Syria, and last month captured their first provincial capital, the city of Raqqa. The also control whole districts of Aleppo.

The government has been hitting the rebel-held areas in the north with airstrikes in recent weeks, reclaiming some of the territory from the rebels, including several villages along the route that links Aleppo with its airport to the city’s east.

The rebels have been trying to capture the airport for months, in hope of having their own airstrip to receive aid flights. The airfield and much of the area around the airport, including an air base, remain under the regime’s control.

More than 70,000 people have been killed in the conflict, the United Nations says.

Kerry, Syrian opposition leader meet

In London, Mr. Kerry was meeting with the opposition’s interim prime minister, Ghassan Hitto, and other senior figures from the Syrian National Coalition.

The Western-backed alliance has been marred by severe divisions in its ranks since its formation late last year in Qatar, and its leaders are mostly seen as disconnected from the myriad rebel forces fighting inside Syria.

The coalition said the candidates are not allowed to have ties to the Assad regime and must be advocates or supporters “of the Syrian revolution.”

In London, Mr. Kerry will have a one-on-one meeting with Russian Foreign Minister Sergey Lavrov later Wednesday. Russia has been Mr. Assad’s staunch ally, supplying Damascus with weapons, shielding the regime from tougher U.N. sanctions and supporting Assad in his resolve to remain in power.

The opposition leaders insist Mr. Assad must step down before they can hold talks with Damascus on a political transition.

During his stop in Israel, Mr. Kerry said the Obama administration was holding intense talks on how to boost aid to Syria’s rebels and that it was important to increase pressure on Mr. Assad’s regime to get it to the negotiating table.

More In: World | International | News