Sheikh Issa Ponda Issa was hit in the shoulder with a tear-gas canister as he tried to escape from officers after being cornered near Tanzania's capital Dar es Salaam.
Kirstie Trup and Katie Gee - both aged 18 and from Hampstead in north London - continue to be treated in Chelsea and Westminster Hospital, where they are ‘well rested and comfortable’.
Faustine Shilogile, a police commander in Morogoro, where the sheikh was shot, said: ‘He has not been arrested. He has been shot at.
'We have been looking for him in all corners of the country. We are now closer to finding who was responsible for this. But this is a serious police investigation. We are doing everything we can.’
The women are spending a third day in hospital after being admitted on Friday. They are receiving treatment for burns inflicted in an unprovoked attack while they were on a volunteering holiday on the island.
Members of both teenagers' families are keeping a bedside vigil, after the pair were flown home and immediately sent to the capital's regional burns centre.
A hospital spokesman said: ‘The patients are well-rested and comfortable at the hospital. They have been with their families all day. Doctors are continuing to assess treatment options for both patients.’
The Foreign Office updated its Tanzania travel advice page on Friday with details of the attack and is warning British nationals to ‘take care’ and read the guidance.
Mr Cash told the Sunday Express: ‘People need to be extra-vigilant and the Foreign Office and High Commission need to make a very thorough evaluation of the threat, as these latest attacks would seem to be on religious grounds.
‘The threat to tourists going to Tanzania and Zanzibar needs to be upgraded, without doubt.’
She is shown wearing an open striped shirt and a silver necklace and what appear to be acid burns are clearly visible on her chin, neck and upper chest.
One of the victim's injuries are much worse than her friend's, it was reported, because helpers used dirty water on her burns.
When ‘they got to the medical centre there was no shower’, he added. ‘They were throwing dirty water at her.’
British tourist Sam Jones told how he desperately tried to help one of the women as the acid burned through her skin following the attack on Wednesday night.
The couple said they supported the injured women by joining them on a private plane to Dar es Salaam for treatment.
Police said five men are being questioned by officers on the Indian Ocean island after the women were attacked by men on a motorbike as they walked along a road.
TUMESHIRIKI NA KUCHAMBUA KUTOKA DM''
Flora Lyimo :Say''
ANYWAY ...KWANINI HAWAJAMSHIKA PALE PALE ? AU NDO ALIISHIA MITINI?? TUNATAKIWA WAHUSIKA KUKAMATWA HARAKA IWEZEKANAYO NA KUFUNGWA KWA MAISHA'' WE DON'T NEED SHAME KAMA HII TO OUR LOVELY TANZANIA JAMANI''' SO SO SAD....I CANT WAIT FOR THOSE DIRTS RATS WALOHUSIKA TO BE BROUGHT TO JUSTICE!!!