The family of a American teenager killed in Yemen during a US attack – a week after his terrorist father also died in a US strike – has lashed out at reports that the young man was a militant.

Abdulrahman al-Awlaki, 16, who was born in Denver, was the son of Anwar al-Awlaki, one of America's most-wanted men, whom an unmanned drone obliterated with a rocket in Yemen last month.

Some US newspapers described the American-born teenager as a militant in the mould of his notorious father, a preacher who was implicated in a series of alleged terrorist plots – including an attempt to bring down an airliner over Detroit – over the past five years.

Yet this week the young man's family, who said Abdulrahman left the US in 2002 when he moved to Yemen with his father, released a statement lashing out at the American media. The teenager's family "watched with surprise" as several newspapers and TV channels "twist the truth" [sic] about the young man," according to the statement. On the night of 14 October, the day Abdulrahman was killed by a US drone, he had "gone barbecuing under the moonlight" with his friends.

Recently posted Facebook photos on a tribute page showed a smiling, cherubic youngster, his glossy brown hair swept into a neat side parting. Others pictured a scrawny young teenager larking around with his friends.

The statement from the Awlaki family claimed the young man had been living in the Yemeni capital Sana'a until several weeks ago, when he disappeared after leaving a note for his mother saying he had gone to search for his father in Shabwah province, the family's ancestral homeland in south-east Yemen.

After the assassination of his father – who was described to one newspaper as "one of the most dangerous al-Qa'ida terrorists" by a US intelligence official – the teenager stayed in Shabwah. He was killed two weeks later.

Speaking to The Washington Post, Abdulrahman's grandfather – Anwar al-Awlaki's father – expressed disbelief that American drones, which have carried out two attacks in Yemen since the end of September, had killed such a young man. "To kill a teenager is just unbelievable, really, and they claim that he is an al-Qa'ida militant," Nasser al-Awlaki, a former Yemeni Agriculture Minister, said. "It's nonsense."

Regardless of whether Abdulrahman was the innocent victim of overwhelming American aggression, his death illustrates the growing signs of an escalation of US influence in the southern Arabian peninsula.

According to Yemeni officials, another victim of Friday's air strike was the Egyptian-born Ibrahim al-Banna, a man the country's Defence Ministry said was head of media for the Yemeni branch of al-Qa'ida.

This group, better known as al-Qa'ida in the Arabian Peninsula (AQAP), has been identified by US intelligence chiefs as the most dangerous terrorist operation in the world. The recent escalation in drone strikes has been seen by some as part of the Obama administration's attempt to drive out its members, who operate in the mountains of the Yemeni highlands. "Everyone with interests in Yemen, including al-Qa'ida and the Americans, is raising the stakes at this time of uncertainty," Abdul-Bari Taher, an analyst, said. "The Americans are wasting no time to try and eliminate the al-Qa'ida threat before the militants dig in deeper and cannot be easily dislodged."