Eyewitnesses have claimed the Tunisian beach massacre may have been carried out by more than one attacker as authorities continue to quiz seven suspected associates of the gunman.
The claims come as an RAF transport plane carrying Britons seriously injured in the shooting landed at Brize Norton, after a brief stop at Birmingham Airport.
David Cameron has declared a national minute's silence for victims of the attack, while Tunisian interior minister Mohamed Gharsalli announced the arrests of several nationals allegedly linked to attacker Seifeddine Rezgui.
Authorities say Rezqui acted alone during the rampage in the resort of Sousse but had accomplices who supported him before, providing him with weapons and logistical support.
But British tourists staying in the north African country claim they saw a second man carrying a gun and roaming the resort.
Steve Johnson, a retired police officer, was on holiday with his wife Valerie and fellow ex-officer Michael Perry and wife Angela.
Mr Perry told the paper he had seen the bare-chested gunman running with a weapon.
When he asked a police officer what had happened to the attacker, he was reportedly told: "We shot him".
Rezqui, dressed in black, appeared to be alone in the video footage of the atrocity that has emerged so far.
The seven people in custody were arrested in at least three different cities and taken for questioning in the capital Tunis.
Yesterday, Mr Cameron announced there would be a nationwide minute's silence at midday on Friday, while Home Secretary Theresa May condemned the "despicable act of cruelty" after she visited the scene of the attacks.
A total of 38 people, including up to 30 Britons, died after 23-year-old student Rezgui opened fire on Friday. The self-proclaimed Islamic State (IS) - also known as Isil - later claimed responsibility.
Announcing the minute's silence, Mr Cameron told MPs: "I know the whole country will want to share in a moment of remembrance."
The Prime Minister, who earlier described the "existential threat" posed by IS as "the struggle of our generation", told the Commons: "We will not give up our way of life or cower in the face of terrorism."
He said Britons were not being advised to stay away from Tunisia's coastal resorts despite the bloody events at Sousse, while he also disclosed that a major exercise will take place in London this week to ensure the UK is prepared to deal with terrorism.
Mrs May laid flowers and observed a period of silence at the scene of the attack and held talks with Tunisian, German, French and Belgian ministers on addressing the threat posed by IS.
Downing Street said all British nationals injured would be returned within the next 24 hours.
Four people needing treatment have been flown back to the UK on board an RAF C17 plane with "medevac" teams experienced at bringing injured service personnel back from operations overseas.
The Ministry of Defence confirmed the plane had landed at RAF Brize Norton in Oxfordshire, after dropping one patient off at Birmingham Airport.
"Patients have now been transferred over to the care of NHS England," a spokesman said.
Meanwhile, tributes have continued to pour in for victims.
A football club said it was "deeply shocked and saddened" by the death of one of its former players and his wife.
Former Birmingham City Football Club player Denis Thwaites and his wife Elaine are reported to have been killed in the attack.
The family of the couple, from Blackpool, Lancashire, appealed for information about their whereabouts.
A 52-year-old man who flew to Tunisia with his wife to celebrate their wedding anniversary has been confirmed dead, his family said.
Philip Heathcote, who lived in Felixstowe, Suffolk, and was originally from Manchester, had been missing feared dead since Friday.
His wife, Allison Heathcote, 48, is in an induced coma after also being shot on the beach. The couple were due to celebrate their 30th wedding anniversary today.
The Prime Minister said the Government was working "as fast as we can" to get information to families still waiting in anguish for news of missing loved ones three days after the attack.
His spokeswoman said delays in identifying the dead are due in part to the fact that the holidaymakers may not have been carrying identification at the time of the attack.
In two cases where authorities "feared the worst", individuals thought to have possibly been victims of the gunman were tracked down alive and well in the UK, she said.
Mr Cameron's spokeswoman said UK authorities were "working closely" with relatives of those killed to offer help with the repatriation of the bodies of their loved ones, and some were expected to be brought home this week.
Holiday firms Thomson and First Choice issued a statement saying they are "aware that some families continue to wait for news of their loved ones".
It added: "We would like to reassure those in this position that we are doing everything we can to provide information as soon as we are able to do so."
Scotland Yard has said more than 1,000 officers are involved in what is its largest counter-terrorism operation since the 7/7 bombings.
US president Barack Obama called Mr Cameron to offer his condolences over the loss of British life and to voice continued American support in the wake of the attack.
"The leaders discussed the importance of working together with countries like Tunisia to tackle the threat posed by Islamist extremism," a No 10 spokesman said.
The British Red Cross has sent four specialist psycho-social volunteers to support British holidaymakers caught up in the attack and has opened a support line for people in the UK on 0844 4631 345.