- Goverment asks residents to vacate battle areas
* Rights group says hundreds of families displaced
* Govt says big offensive against insurgents yet to come
By Ibrahim Mohamed and Abdi Sheikh
MOGADISHU, March 11 (Reuters) - The death toll from two days of fighting in Somalia's capital between government forces and al Shabaab rebels has risen to 54, ambulance services said on Thursday as clashes subsided with both sides claiming successes.
The government urged residents to vacate the areas where fighting had taken place as it planned to take on the rebels again, but said it had not yet started a long-awaited offensive to dislodge the insurgents from Mogadishu once and for all.
"The government was just counter-attacking the rebels. We are going to fight the rebels as planned, let civilians around those areas vacate," Abdirisaq Mohamed Nur, Mogadishu's mayor, told reporters.
Insurgents have fought the government since the start of 2007 and the Western-backed administration has been hemmed into a few blocks of the capital since a rebel offensive last May.
"We have carried 54 dead people and 140 others injured yesterday and today," Ali Muse, coordinator of ambulance services, told Reuters.
Earlier in the day the Elman human rights group had put the death toll at 38 and 104 wounded.
"The death toll may rise because the shelling was terrible. Hundreds of families have been displaced from at least four districts of Mogadishu," Ali Yasin Gedi, vice chairman of the group, told Reuters.
RESIDENTS SPOT HELICOPTER, PLANE
Somalia has lacked an effective central government for 19 years and Western nations and neighbouring countries say the anarchic country provides sanctuary for militants intent on launching attacks in east Africa and further afield.
Both sides claimed victory after the fierce battles in the capital that had died down by late Thursday.
"We drove away al Shabaab and captured most of their strongholds in the north of Mogadishu," Sheikh Yusuf Mohamed Siad, Somalia's state minister for defence, told Reuters.
Al Shabaab's spokesman said his fighters had set ablaze an armoured vehicle belonging to African Union troops.
There was no immediate comment from the AU Amisom force of more than 5,000 troops based in the capital.
Outside the capital, much of southern and central Somalia is controlled by al Shabaab -- an al Qaeda-linked militia that wants to impose its own harsh version of sharia law in the country -- and another insurgent group, Hizbul Islam. Somali-based pirates have extracted huge ransoms by hijacking international shipping.
Residents of the southern port town of Kismayu and Dhobley near the border with Kenya -- which are both controlled by al Shabaab -- reported having seen a helicopter and a larger plane overhead several times over the past few days.
"Al Shabaab fired guns at them but they were beyond reach," Sugaal Kusow, a Kismayu resident, told Reuters. "They were not bombing us, so we assumed they are monitoring planes." (Additional reporting by Abdi Guled; Editing by George Obulutsa, David Clarke and Mark Trevelyan)