BEIRUT – Syrian rebels made a new push into Damascus on Wednesday, clashing with troops in the rebellious suburbs of the capital and firing mortars at a presidential palace and a Palestinian refugee camp, activists said.

The regime stronghold of Damascus has seen a surge in violence this week with some of the fiercest clashes in months. In recent days, opposition fighters also stepped up assaults on high-ranking supporters of President Bashar Assad in the capital.

The rebels also have been trying to break the resistance of a pro-government Palestinian faction, which could drag the half million Palestinian refugees in Syria into the civil war.

The new challenge from rebels in the capital comes as the U.S. and Britain take steps to bolster the fragmented Syrian opposition. British Prime Minister David Cameron said his government planned to change its policy and deal directly with opposition military leaders.

Previously, Britain has had contacts only with exile groups and political opposition figures inside Syria.

Cameron urged newly re-elected President Obama to join Britain in opening direct talks with rebel fighters, and said they must do more to end the civil war that has killed more than 36,000, according to activists’ tallies.

Rebels fired several mortar rounds at the Syrian president’s residence in the Muhajireen neighborhood in central Damascus on Wednesday morning, but failed to hit their mark, said Bassam al-Dada, an adviser to the commander of the Free Syrian Army, Col. Riad al-Assad.

“This was a very special operation that was planned for a while,” al-Dada said by telephone.

There are two presidential palaces in Damascus — the Muhajireen Palace and the People’s Palace, which is on Mount Qasioun, overlooking the capital.

Before the uprising began last year, Assad spent much of his time at the Muhajireen Palace.