* African peacekeepers fighting Qaeda-linked insurgents
* U.N. chief says funds needed to support Somali army
* Somalia in chaos since civil war broke out in 1991
By Drazen Jorgic
NAIROBI, March 12 (Reuters) - African Union peacekeepers and the Somali army have begun a major offensive against al Shabaab militants, the U.N.'s Special Representative to Somalia said on Wednesday, urging donors to fund logistical support.
U.N.-backed peacekeepers pushed the Islamist fighters out of Mogadishu in 2011, but the al Qaeda-linked group has continued to launch guerrilla-style attacks there and kept control of several towns and many rural areas.
A new offensive to capture the remaining territory had been expected ever since the U.N. Security Council in November authorised an increase of more than 4,000 peacekeepers for the African peacekeeping force known as AMISOM, from Ethiopia, Kenya, Uganda, Burundi and Sierra Leone.
Special Representative Nick Kay said the push started this month when Ethiopian troops took control of towns in southern Somalia, including Bakool regional capital Hudur.
"(The offensive) is progressing quite well," Kay told Reuters via telephone from Mogadishu.
"The Ethiopians clearly have been doing well, recaptured several important towns in Bakool and in Gedo (region)."
Kay said al Shabaab had to be pushed out of territory where it was training more insurgents, taxing businesses and importing arms through ports.
"That's why this AMISOM and Somali National Army (SNA) offensive is really important to deprive them of those bases," Kay said.
In a rare move, the U.N. has passed a resolution to provide logistical support to the SNA troops fighting alongside the 22,000-strong AMISOM force, which has been in Somalia since 2007.
Kay said this support will see one U.N. agency carry out medical evacuations and provide rations, transport and tents for the Somali army, which analysts say is badly trained, poorly equipped and lacks discipline.
The U.N. Support Office for AMISOM (UNSOA) needed more funding to do its job and so far only Britain and United States have pledged a total of about $6.5 million, Kay said.
"The rule of thumb was that, to begin with at least, $20 million would be a good amount to keep going," he added.
Al Shabaab has carried out several bombings in Mogadishu in recent months, including a large-scale raid on the Somali presidential palace and an attack on a U.N. convoy.
Kay warned conditions were likely to remain volatile in the capital and al Shabaab might intensify its bombing campaign as it came under pressure in the countryside.
"I think that's something AMISOM, the government and ourselves are prepared for," he said. "Things may get tougher in the short term but we have to be ready for that." (Editing by Andrew Heavens)