* U.N. says three children dead after explosion
* Muslim communities "besieged" by Christians - UN
* EU has delayed mission to send troops (Adds detail and context throughout)
BANGUI, March 28 (Reuters) - Eleven people died in the capital of the Central African Republic after a grenade exploded among mourners gathered for a funeral, the Red Cross said on Friday, in what residents said was an attack on Christians.
Tit-for-tat inter-communal violence in the impoverished, landlocked country has intensified in recent days as Christian militia have become more militarised, aid workers say.
Two thousand French soldiers and 6,000 strong African Union peacekeeping mission have failed to stop the raging violence in the landlocked, impoverished country that has killed thousands.
Residents told Reuters a Muslim tossed a hand grenade at a crowd in a Christian district of Bangui's PK5 neighbourhood on Thursday night. Antoine Mbao Bogo, head of the local Red Cross, said that 11 people were killed, including both those who died instantly and later in hospital.
The United Nations Children's Fund (UNICEF) said that three of the dead were children.
Mainly Muslim rebels from the north known as Seleka seized power a year ago in Central African Republic. Their rule was marked by a string of abuses on the majority Christian population, triggering waves of revenge killings that left thousands dead and displaced hundreds of thousands.
The former rebels quit power in January under international pressure, giving way to an interim civilian government. But it has been powerless to halt attacks on Muslims by Christian militia known as anti-balaka intent on driving them from the country.
Heavy and light arms fire has rung out most nights this week while armed Christian militia known as anti-balaka are manning checkpoints across Bangui, according to a Reuters witness.
"The status quo is bound to deteriorate further," said Christoph Wille of the Control Risks consultancy.
"The country is now effectively divided into a northeast held by former Seleka rebels, a capital controlled by international troops and a the rest in the hands of a loose alliance of anti-balaka militias."
The United Nations estimates that about 15,000 Muslims are still trapped in Bangui and the surrounding countryside.
Volker Turk, of the U.N. refugee agency, said that anti-balaka elements were becoming more militarised and had "besieged" the Muslim population in the town of Boda.
The African Union branded the Christians targeting Muslims as "terrorists" this week, a day after a Congolese peacekeeper was killed.
In a sign of deteriorating security conditions, some of Bangui's displaced have started flocking back to make-shift camps, after briefly returning to their homes in recent weeks.
U.N. aid agency OCHA said that the number of internally displaced in Bangui has increased by more than 20,000 to 200,000 since 12 March.
"Many residents feel trapped - unable to stay, but also unable to leave," said Philippe Bolopion, United Nations director at Human Rights Watch.
"They risk being lynched or attacked on the street if they try to go to another neighbourhood or to move outside of Bangui."
The European Union has pledged to send up to 1,000 peacekeepers to help protect the displaced. But the plan has been delayed because of the failure of European governments to provide key soldiers and equipment. (Reporting by Serge Leger Kokpakpa and Emma Farge; Editing by Tom Heneghan)