Brig. Gen. Mustafa al-Sheikh, who heads the FSA's Military Council, told The Associated Press that the group made the move last week. He would not say where the new headquarters is located or give other details.
The FSA is the most prominent of the rebel groups trying to topple Assad, though its authority over networks of fighters in Syria is limited. Its commanders have been criticized for being based in Turkey while thousands are killed inside Syria.
Despite the announcement of the command move, rebels still have to rely on Turkey as a rear base for supplies and reinforcements. In the past few months, rebels have captured wide swaths of Syrian territory bordering Turkey, along with three border crossings, allowing them to ferry supplies and people into Syria.
FSA commander Col. Riad al-Asaad announced the move of the command center in a video with the title "Free Syrian Army Communique Number 1 from Inside." Wearing a military uniform and surrounded by a dozen gunmen, the commander said the aim is to "start the plan to liberate Damascus soon, God willing."
Al-Sheikh, the other top FSA commander, said moving the command "will speed up the fall of the regime because it will give a big boost to the morale of rebels and there will be a command to follow-up on operations."
"There are liberated areas now and it's better for the command to be with the rebels instead of being abroad," al-Sheikh said in a phone interview from Turkey. The general said he has been going back and forth to Syria.
In recent months, rebels have succeeded in taking the fight to Damascus, but the regime has reasserted control in many areas. In the summer, rebels also launched an offensive on Syria's largest city, Aleppo, and are holding several neighborhoods there, despite daily battles with regime forces.
Activists say nearly 30,000 people have been killed since Syria's crisis began in March 2011. The uprising began with largely peaceful protests against Assad's regime, but has since morphed into a civil war in the face of a brutal government crackdown.
The Syrian conflict has increasingly spilled into neighboring Turkey, Jordan and Lebanon, with several hundred thousand Syrians seeking refuge there and battles occasionally being fought along Syria's borders.
On Saturday, the Turkish military deployed three howitzers and an anti-aircraft gun near Tal Abyad, a Turkish-Syrian border crossing captured by the rebels earlier in the week, the Turkish news agency Dogan reported. Dogan video showed at least three large military trucks towing the guns along a highway.
On Saturday, an Associated Press reporter heard at least six mortar shells fall in the area. The crossing was in the hands of rebels who held eight detainees there, including three Syrian border inspectors, but released them later.
Turkey also reinforced its border with anti-aircraft missiles after Syrian forces brought down a Turkish jet on June 22, and it threatened to target any approaching Syrian military elements. Turkey said its plane was in international airspace, countering Syrian claims that it was in Syrian airspace.
Also Saturday, Lebanon's army said Syrian rebels attacked one of its positions in the mountain town of Arsal and that its forces drove the rebels away without causing casualties.
The military did not give a reason for why the rebels might attack a Lebanese position. In the past, Syrian government forces have fired shells or missiles across the border. Lebanese pro- and anti-regime groups have also clashed.
Rebels, many of them Sunni Muslims, are known to cross to and from areas in Lebanon that are predominantly Sunni, like Arsal. In recent months, the Lebanese army has tried to stop them by setting up new positions and sending troops.
Syria's activist networks, which monitor the country's violence, were not aware of the fighting.
On Syria's border with Jordan, rebels assaulted a Syrian air defense base and were pushed back, activists said. A Jordanian government minister said Jordanian border guards captured several gunmen on the Jordanian side, but it was not clear if they were rebels.
The fighting in and around the Syrian border town of Nasib continued until dawn Saturday, Jordan's state-run news agency Petra said. Nasib is in the southern province of Daraa, where the uprising began in March 2011.
The Britain-based Syrian Observatory for Human Rights said there were casualties on both sides, but did not give figures.
In Damascus, an umbrella opposition group, the National Coordination Body for Democratic Change in Syria, said it is postponing a conference that would have been the largest gathering of anti-regime representatives in the country since the uprising began.
The group has said two of its leaders disappeared after arriving at Damascus International Airport on Thursday, along with a friend who was to pick them up. It blamed the regime for the disappearance. The state-run news agency SANA quoted the Interior Ministry as saying "terrorist groups" kidnapped the three, using the term it employs for rebels, and that a search has been launched.
Some Syrians had hoped that the conference might result in a unified opposition voice inside Syria that could credibly negotiate with the regime.