* Fighting has been going on since S.Sudan secession
* Peace efforts by African Union undermined
KHARTOUM, Feb 28 (Reuters) - Sudan is sending reinforcements to Blue Nile state to fight rebels near the border to South Sudan, state-linked media said on Thursday.
Last week, the Sudan People's Liberation Movement-North (SPLM-North) said it had launched an offensive to take Kurmuk near the border to South Sudan and Ethiopia.
Sudan's army has been fighting rebels of the SPLM-North in Blue Nile and nearby South Kordofan state since around the time of South Sudan's secession in July 2011 under a 2005 deal which ended decades of civil war.
The fighting undermines efforts by the African Union to secure the poorly defined border and end tensions between the neighbours which came close to war in April. Sudan accuses South Sudan of backing the SPLM-North, a claim denied by Juba.
On Thursday, the Sudanese Media Centre said an infantry battalion had arrived in Blue Nile's capital Damazin, where two more battalions would be expected in the next few days. The state's main airport is in Damazin.
It said the troops had arrived to "strengthen security" in the state and for a campaign of "cleansing", a term authorities use to describe fighting rebels.
The SPLM-North, whose fighters sided with the South during the north-south civil war, said this week its troops were inside Kurmuk town, a claim denied by the army. The SPLM had lost the town in autumn 2011.
Kurmuk is strategic for both sides because it was a stronghold of southern fighters during the civil war. Its loss would be a setback for Sudan, which has been trying to develop the resources of Blue Nile.
The state is rich in chrome and is a production site for gum arabic, used in soft drinks.
South Sudan accused Sudan two weeks ago of building up troops near the border, much of which is disputed.
The African Union brokered a deal in September to defuse hostilities between the two countries. But neither side has withdrawn its army from the zone or revived oil exports from the landlocked South Sudan through Sudan, as agreed in Addis Ababa.
The Sudanese foreign ministry said in a statement it was committed to implementing the September deal. (Reporting by Ulf Laessing; Editing by Michael Roddy)