Relatives of the only man convicted of the Lockerbie bombing are to launch a fresh bid to clear his name more than two years after his death.

Six immediate members of Abdelbaset al-Megrahi's family have joined forces with a number of British relatives of those who died in the atrocity to seek a third appeal against his conviction in the Scottish courts, a press conference in Glasgow heard.

On Thursday they lodged an application with the Scottish Criminal Cases Review Commission (SCCRC), the body that reviews alleged miscarriages of justice in criminal cases and has the power to refer a case back to the high court.

Megrahi was the sole person found guilty of the bombing of Pan Am flight 103 over Scotland on 21 December 1988, in which 270 people were killed.

The Libyan abandoned a second appeal against his conviction in 2009 after being diagnosed with terminal prostate cancer.

He was later released from jail by the Scottish government on compassionate grounds and died protesting his innocence in May 2012.

Solicitor Aamer Anwar said that more than a quarter of a century after the atrocity "the truth remains elusive".

Speaking in Glasgow, he said: "The case being lodged this morning seeks to overturn the conviction of Abdelbaset al-Megrahi for murder."

Dr Jim Swire, left, the father of Flora Swire who died in the Lockerbie bombing, with solicitor Aamer Anwar. Photograph: Andrew Milligan/PA

The solicitor said the three volumes of papers which form the basis of the new application will be delivered to the SCCRC later .

He has been instructed by 24 British relatives of victims and six immediate family members of Megrahi who, for safety reasons, are not being identified.

Over the 25 years since the bombing and Megrahi's subsequent conviction, there have been many legal twists and turns in the case which have brought his family to this point.

Some of the victims' families believe Megrahi was rightly found guilty, and prosecutors at the Crown Office in Scotland insist they do not fear scrutiny of the conviction and would rigorously defend it.

But others, including some of the British relatives, argue that the Libyan was wrongly put behind bars and that the truth about who murdered their loved ones remains elusive.

Megrahi was found guilty of mass murder following a trial at Camp Zeist in the Netherlands in 2001 and jailed for life with a minimum term of 27 years. He lost his first appeal in 2002.

The following year, he applied to the SCCRC for a review of his conviction. An investigation costing £1.1m by the body led to a finding in June 2007 of six grounds where it believed a miscarriage of justice may have occurred.

This decision opened the door to Megrahi's second appeal against his conviction. Although a number of hearings had already been held before senior appeal judges, he dropped his appeal two days before being released from prison in August 2009.

Despite the guilty verdict and Megrahi's decision to drop the appeal, campaigners and families of victims are still dealing with the impact, and a number of them have been considering another appeal for some time.

Last month, it emerged that a new application for the conviction to be looked at again was soon to be handed to the SCCRC by campaigner Jim Swire, representing more than 20 British relatives of bombing victims.

Swire, whose 23-year-old daughter Flora died in the bombing, has long held the view that Megrahi was not guilty of the atrocity.

The fact that Megrahi's own family has now chosen to take forward a fresh appeal bid could boost its chances of getting back to court.

Swire has previously said Megrahi's family could risk their lives by raising the prospect of launching a fresh appeal against conviction.

Swire said he wrote to those families whose addresses he still held and asked whether they wished to support the application, with 23 responding positively.

Anwar said: "The number is growing on a daily basis. Each name will be added to the application to the SCCRC."

The solicitor said he expected to meet with the board next month and it would be several months before the body made a decision on whether it will accept the case.