Joseph Kony is one of several rebel commanders wanted for war crimes by the International Criminal Court.

Mr Museveni said Mr Kony had until the end of July to end the war and said the government would guarantee his safety.

The LRA has abducted thousands of children and forced them to fight since the conflict in the north began.

According to a press release from State House, during a meeting with British overseas development minister Hilary Benn, the Ugandan president said the rebel leader had until the end of July to end the war peacefully.

"If he got serious about a peaceful settlement, the government of Uganda would guarantee his safety," the statement added.

But the BBC's Will Ross in Kampala this may well be easier said than done.

After years of brutal attacks on civilians, the ICC intends to prosecute Joseph Kony and other LRA commanders for war crimes - if they can be captured.

So offering an amnesty to these rebel leaders may not be legally possible, our reporter says.

Sudanese government officials have recently met the rebel leadership, but past attempts to negotiate an end to the war have failed, with both the Ugandan government and the rebels being accused of lacking commitment to peace talks.

The LRA has been weakened by a military offensive, but in recent months, the rebels have spread across southern Sudan and into the Democratic Republic of Congo.

Meanwhile, some displaced Ugandans are returning home, but sporadic attacks in northern Uganda continue to keep some 1.5m people in squalid camps.