BEIRUT — Two booby-trapped vehicles exploded within hours of each other Friday in Syria’s once-impregnable capital of Damascus, killing at least five police officers as rebels increasingly target President Bashar Assad’s seat of power.

With the civil war intensifying, the head of the Red Cross warned after meeting with Assad that the situation in the country was rapidly deteriorating. Elsewhere in Damascus, shells struck a Palestinian refugee camp, killing 10 people, state media said.

Damascus was relatively quiet until July, when rebels launched a bold attack, capturing several neighborhoods and setting off a bomb that killed four high-ranking security officials, including the defense minister and Assad’s brother-in-law.

Since then, the regime has succeeded in largely quelling a rebel offensive in the capital, but has struggled to contain an opposition push into the northern city of Aleppo, the country’s commercial hub.

Friday’s first blast in Damascus killed five officers when a motorcycle packed with explosives blew up across the street from a mosque in the Rukneddine neighborhood, state television said. An Associated Press reporter at the scene said the bomb damaged a nearby medical clinic, staining its walls and the pavement with blood.

There were no casualties in the second blast, a car bomb that went off about two hours later in the upscale Mazze neighborhood near the Ministry of Information and the Ministry of Justice, which are about 330 feet apart. Friday is the weekend in Syria and institutions are usually closed.

State television blamed terrorists, the term the regime uses to describe the rebels. There was no immediate claim of responsibility for the attacks.

The blasts came five days after two bombs exploded near the offices of the Syrian military’s joint chiefs of staff in Damascus, slightly wounding four officers.

Peter Maurer, the new president of the International Committee of the Red Cross who just returned from a three-day trip to Syria, said he was shocked by the ‘‘immense destruction’’ he saw there.

‘‘Since the conflict erupted, there have been many casualties, and now the situation is rapidly deteriorating even further,’’ Maurer said in Geneva on Friday. He said he held positive talks with Assad to gain access to detainees and free up deliveries of badly needed aid.

The uprising began in March 2011, when protests calling for political change were met by a violent government crackdown by government troops. Many in the opposition took up arms, and activists say more than 23,000 people have been killed. The government says more than 4,000 security officers are among the dead.

Assad has made similar commitments in the past to other officials.

Syrian state media reported earlier this week that Assad told Maurer that the Red Cross is welcome to operate on the ground in the country as long as it remains ‘‘neutral and independent.’’ Assad blames international powers for fomenting the country’s uprising.

‘‘The positive commitments I received during my meetings will obviously have to be followed up and tested in the coming weeks,’’ Maurer said Friday. ‘‘Each day that passes brings more casualties and human suffering.’’

In other violence Friday, several people were either killed or wounded when a Palestinian refugee camp in Damascus was shelled, activists and state media reported.

The Local Coordination Committees said Syrian troops shelled the Palestinian refugee camp of Yarmouk. State-run Syrian television confirmed violence in the camp but blamed ‘‘armed terrorists’’ firing rockets into the camp, killing 10 people. It added that troops were chasing the gunmen.

At least 60 people were killed Friday around the country, from Idlib and Aleppo in the north to Deir el-Zour in the east to Hama and Homs in the center as well as Daraa to the south, activists said.