Smoke rises from Damascus suburbs of Ain-Terma, during clashes between Syrian rebels and pro-government forces August 28, 2012. \ (STRINGER/REUTERS)

Syria’s President Bashar al-Assad claimed Tuesday to be gaining ground in the bloody conflict that has racked the country for nearly 18 months, offering an assessment that appeared to be backed up by developments on the ground.

“We’re fighting a battle both locally and internationally,” he said in an interview with state TV. “So we might need time to win it. But I can say one sentence: We’re heading forward. The situation is better now, but the end is not there yet. That needs time.”

The brief video clip released Tuesday featured one part of an interview that state TV said would be aired in full Wednesday night.

Assad’s comments came after ramped-up attacks in and around Damascus over the past week that have killed hundreds of people — including at least 320 in a single suburb Saturday, according to opposition groups — and that seem to have shifted the momentum toward government forces. The fighting in Aleppo, Syria’s biggest city and commercial hub, meanwhile, appears to have bogged down.

On Tuesday, the Syrian military scattered fliers across Damascus from helicopters, warning rebel forces to either surrender or die, in a possible sign of an even more serious escalation in the violence in the capital.

In the video clip released Tuesday, Assad also took a jab at Turkish leaders who have called for his ouster, and declared that the Turkish public supports his government.

“Do we go backwards because of the ignorance of some of the Turkish leaders?” he asked. “Or do we look at our relationship with the Turkish people, especially since these people stood with us in this crisis against all odds.”

Syria’s neighbors are increasingly feeling the effects of the conflict in the country as more civilians flee the intense fighting. About 5,000 people a day have been arriving at the border with Turkey in the past two weeks, and the number of refugees at the Jordanian border has more than doubled in the past week from 4,500 to 10,200, the Office of the U.N. High Commissioner for Refugees said Tuesday.

The number of unaccompanied children crossing into Jordan has also jumped, the U.N. agency reported, and some refugees said they had been displaced five or six times before crossing the border.

“Some of those who have crossed in recent days, especially Friday, report being bombed by aircraft,” agency spokeswoman Melissa Fleming said at a media briefing in Geneva. “There are also reports of shelling, mortars and other weapons fire.”

Also Tuesday, a car bomb exploded during a funeral in southeastern Damascus, killing 12 people and injuring 48, Syrian state media reported.

The state-run Syrian Arab News Agency (SANA) attributed the attack to “terrorists” and noted that the funeral, in the mixed Christian and Druze area of Jaramana, was being held for two people who had died in an explosion Monday. Photos posted by SANA showed the charred and mangled shells of several cars beside demolished cinder-block walls.

A spokesman for the rebel Free Syrian Army said the attack could have been carried out by government forces. “The regime is trying to create sectarian discord,” Col. Aref Hammoud said. “They want to send a message that ‘if we go, these minorities are in danger.’ ”

Earlier in the day, three members of a family, including a young girl, were injured by a bomb attached to their car in the same area, SANA reported. Hammoud denied that rebel forces were involved in either blast.

Among the fliers that were dropped over Damascus on Tuesday was one labeled a “safe passage card,” which noted that any rebel fighter who showed up with the flier, and unarmed, at a government-run checkpoint would be treated humanely and taken into custody.

Others were more threatening. “You either die a dishonorable death,” one flier warned, “or you leave your weapons and return to the embrace of our great country.”

A Free Syrian Army fighter in Damascus said the fliers were probably aimed at swaying ordinary Syrians who do not fully support either the government or the rebels. But, he argued, the recent killings were sending a much louder message than the fliers about the government’s intentions.

“Total cleansing of the cities — I think this is their new strategy,” said the fighter, who uses the nom de guerre Majd al-Shami. “They want to kill everyone to stay in power now.”

The Syrian military also kept up its offensive in other parts of the country Tuesday. Airstrikes in the western city of Kafr Nabel left at least 23 people dead, according to the Local Coordination Committees activist network.

Video apparently recorded shortly after the attack in Kafr Nabel shows several cars on fire in the middle of rubble-strewn streets as groups of men carry wounded people covered in blood from the scene.

On Monday, the United States declined to endorse a call by French President Francois Hollande for the Syrian rebels to form a provisional government to be given international recognition. Hollande, the first Western leader to seek a shadow government in Syria, said he hoped that global unity would heighten the pressure on Assad to step down.

Ahmed Ramadan and Suzan Haidamous contributed to this report.