Tunisia's interior minister has said a group of suspects associated with the beach resort gunman have been arrested by authorities.

38 people, including three Irish people, were killed when Seifeddine Rezgui (24) opened fire as they sunbathed on the beach in the resort town of Sousse.

Authorities have been investigating whether he was working alone or if he had accomplices.

Interior Minister Najem Gharsalli did not give further details about the arrests but said officials were still verifying whether Rezgui had been trained in jihadist camps in neighbouring Libya.

Islamic State has claimed responsibility for last Friday's assault on the Imperial Marhaba hotel.

"We have started by arresting a first group, a significant number of people, from the network that was behind this terrorist criminal," Mr Gharsalli said at a joint press conference with his German, French and British counterparts.

He did not give numbers but said everyone arrested is Tunisian and the investigation remained in its early stages.

"We will find all those involved, whether it was just logistical support or not," he added.

A Dublin couple caught up in the terrorist attack say its nothing short of a miracle that they are still alive.

Anthony and Betty Tunstead were in their room when they heard the gunfire on the beach.

They had been holidaying with Betty's sister and her husband Denis.

The foursome had made friends with Larry and Martina Hayes, who were staying in the same hotel.

Mr and Mrs Hayes were among 38 people killed on Friday when gunmen opened fire in the resort of Sousse.

They told Today FM they knew at an early stage it was bad news.

Tributes have been paid to the three Irish citizens who died in the tragedy. Lorna Carty from Co Meath died after she went sunbathing on the beach.

The mother-of-two had gone on holiday with her husband, who was recovering from heart surgery.

Dunderry Gaelic Athletic Association (GAA), where her husband Declan was treasurer and her son Simon and daughter Hazel represented at football, hurling, and camogie, paid tribute.

A statement said: "Our thoughts and prayers are with the family and friends of Lorna Carty. Lorna was always there to give a helping hand with all of our teams and events. She was greatly loved in our community and will be dearly missed."

Laurence (Larry) and Martina Hayes lived in Athlone, Co Westmeath. Mr Hayes had worked for Bus Éireann for the last 20 years as a schools transport inspector.

A spokeswoman for Bus Éireann said: "The company wish to extend its deepest sympathies and condolences to the family and friends of Larry Hayes and his wife Martina."

She said Mr Hayes was "highly regarded on both a personal and professional level" by all his colleagues at Bus Éireann.

A Tunisian police officer on horse patrol the beach in front of the Imperial Marhaba Hotel in Sousse, Tunisia. Image: Darko Vojinovic / AP/Press Association Images

The attacker's father and three of his university roommates were detained and questioned in the capital Tunis before being released.

A phone found by a swimmer reportedly showed the gunman called his father shortly before the devastating assault.

But Hakim Rezgui has reportedly said he was "shocked" by his son's actions and did not know who "put these ideas in his head" and "warped his mind".

He said he was "really sorry", was "so ashamed" and felt like he had died along with the victims.

Rezgui was an old aviation student who was previously unknown to Tunisia's counter-terrorism officials and appears to have been radicalised in the last six months.

Just how that happened will be the focus of the Tunisian investigation into the shooting.

Islamic State has claimed responsibility for the attack - and in Twitter messages, referred to Rezgui using the jihadist pseudonym Abu Yahya al Qayruhni.

Rezgui had never travelled abroad in his lifetime, prompting fears that he was radicalised at home, potentially at a local mosque.

At least 30 British killed

The number of British people killed in the Tunisia terror attack is expected to double to at least 30.

The British government has already confirmed 18 of the 38 victims who died in the deadly rampage by the gunman Seifeddine Rezgui were from the UK.

Footage has also emerged of Rezgui sprinting along the shore with his Kalashnikov after opening fire on tourists.

Interior Ministry spokesman Mohamed Ali Aroui said: "We are sure that others helped, but did not participate. They participated indirectly."

As well as providing the weapon, investigators also believe the suspected accomplices helped get Rezgui get to the scene.

A minute of silence will be held nationwide in the UK on Friday to remember the victims of the Tunisia terror attack, the prime minister has said.

The act of remembrance will take place at noon, one week on from the beach massacre that killed dozens of Britons, David Cameron told the House of Commons.

Mr Cameron said the victims of Rezgui's attack were "innocent" people who had saved up for time away with family and friends, who "suddenly became the victims of the most brutal terrorist attack against the British people for many years".

He told MPs a memorial to the victims of the attack would be announced in due course.

For now, he said his government's priority was bringing back those Britons who have been injured and those who have died.