Jamal Khashoggi’s sons have appealed to the Turkish and Saudi authorities to find and return their father’s body for a family burial, as more details emerged about alleged Saudi attempts to cover up the truth about the dissident journalist’s killing.

Salah, 35, and Abdullah, 33, broke their silence a month after their father disappeared at the Saudi consulate in Istanbul in an interview with CNN on Sunday, describing how difficult the last few weeks had been for the family and paying tribute to a man they called “courageous, generous and very brave”.

Salah, who was believed to have been subject to a travel ban preventing him form leaving the kingdom, flew to Washington DC with Abdullah, their two sisters and respective families two weeks ago, just after he was pictured shaking hands with Crown Prince Mohammed bin Salman after being summoned to one of Riyadh’s royal palaces.

Play Video 1:09 Fiancee says Jamal Khashoggi was worried about visiting Saudi consulate - video

It is alleged that the powerful heir to the throne must have at a minimum been aware of the plan to kill Khashoggi, who had become increasingly critical of the Saudi royal family since moving to the US in self-imposed exile in 2017.

When asked about his meeting with Prince Mohammed, which was widely criticised as a royal attempt at damage control, Salah said the visit had been “over-analysed”.

The family is waiting for the results of the investigation into their father’s killing to emerge and trusts King Salman to bring the perpetrators to justice, he added.

The Turkish president, Recep Tayyip Erdoğan, and officials from his ruling AK party have reiterated their belief in recent days that the “highest levels” of the Saudi establishment must have ordered the journalist’s killing, as well as allegations that Saudi Arabia is incapable of carrying out an independent and unbiased criminal investigation.

Facebook Twitter Pinterest Saudi Crown Prince Mohammed bin Salman (right) meets Salah bin Jamal Khashoggi in Riyadh on 23 October. Photograph: Bandar Algaloud Handout/EPA

Riyadh’s explanation for what happened to Khashoggi has changed several times. After two weeks of denials that the kingdom had anything to do with the journalist’s disappearance, Saudi officials said that he had been killed during a fight with a team of rogue extradition agents, who had been arrested. A week later Saudi Arabia said the evidence compiled by Turkish investigators actually showed his killing had been “premeditated”.

The kingdom maintains that Khashoggi’s body was wrapped in a rug and disposed of by a “local collaborator” who has not been identified.

His remains have still not been found – and Turkish investigators allege his body was cut up with a bone saw and either disposed of in rural areas outside the city or dissolved in acid in a garage under the nearby consul general’s house.

On Monday, Turkish newspaper Sabah, citing unnamed officials, said new evidence in the case showed that Khashoggi’s body had been removed from the consulate in five suitcases, and that an 11-member team of Saudi investigators that arrived in Turkey nine days after he disappeared included a chemical expert and a toxicology expert, who removed evidence of the killing.

Investigators found freshly painted surfaces during an initial search of the consulate building.

Turkish officials have steadily leaked details from the investigation to local media, a strategy designed to keep up pressure on Prince Mohammed.