London, June 19 (IANS): Islamic State militants have executed three fighters accused of defecting to the Taliban as a brutal turf war escalates between the rival organisations in Afghanistan.

The killings come days after the Taliban sent a letter to IS warning them to stay out of the country, saying there was room for only "one flag, one leadership" in their fight to re-establish strict Islamist rule, a Daily Mail report said.

One video posted on pro-IS accounts shows a line of armed fighters standing behind two kneeling men who are shot dead by one of the militants with a handgun.

In a separate execution, pictures appeared to show another alleged defector being beheaded.

The groups declared war against each other in April after the Afghan Taliban branded IS's self-declared caliphate illegitimate and refused to declare allegiance to its leader Abu Bakr al-Baghdadi.

IS responded by launching recruitment drives deep into Taliban territory, allowing them to expand rapidly -- even reportedly replacing the Taliban as the dominant controlling force in one district.

The warning letter from the Taliban came amid heavy fighting this week in eastern Afghanistan between the Taliban and breakaway factions who now swear allegiance to IS, which in the past year seized large swathes of Iraq and Syria.

The entry of IS, while its numbers remain small, has complicated Afghanistan's already escalating war following the withdrawal of most foreign troops at the end of last year.

The letter addressed to Al-Baghdadi said the Taliban "based on religious brotherhood asks for your goodwill and doesn't want to see interference in its affairs".

The Taliban have fought to topple Afghanistan's Western-backed government since the US-sponsored military intervention that toppled their own five-year rule in 2001.

The letter to Al-Baghdadi, signed by Taliban political committee chief Mullah Akhtar Mansoor, shows the insurgents also were worried.

"Jihad against American invaders and their slaves in Afghanistan must be under one flag, one leadership and one command," it said.

The letter also appeared intended to dissuade other Taliban fighters considering switching sides.

Besides Arabic, it was written in Dari, Pashto and Urdu languages that are spoken in Afghanistan and Pakistan and was distributed by an official Taliban spokesperson.