In the video, which was released on Sunday and reported by jihadist monitoring group SITE Intelligence Group, the Abu Sayyaf terrorists force Sekkingstad to appeal to the Norwegian government for help.
“Contact this group through June at the Canadian embassy and try to negotiate with this group," Sekkingstad says in the video, according to SITE. "We will executed on June 13 at 3 o'clock, unless there is an agreement made with this group."
The Norwegian man's fellow hostages, Canadian Robert Hall and Filipina Marites Flor, make similar on-camera pleas. All three hostages were also forced to appeal to Filipino president-elect Rodrigo Duterte for help.
The terrorist group said earlier this month that at least one hostage will be murdered if a ransom is not paid by June 13th. Abu Sayyaf -- whose leaders have sworn allegiance to the Isis terror group -- have demanded 600 million pesos ($12.8 million) for the hostages' release.
Norwegian terrorism expert Jan Oskar Engene told NTB that the new video “is very serious for the hostages”.
“It was already very serious and I don't know what can change it. If the ransom demand is as high as it has been, there is a small chance that it will be met,” he said.
In April, the group killed Canadian John Ridsdel after a previous ransom deadline passed.
A spokesman for the Norwegian Ministry of Foreign Affairs said that the ministry was aware of the new video warning but would not go in to details.
“We are working on contributing to the best possible solution in this case. The most important thing for us is the lives and health of the hostages and the interests of their relatives,” press chief Rune Bjåstad told NTB.
Engene said there is little chance that Norway will meet the Islamists' ransom demands.
“Seen in isolation, it would resolve the matter for this hostage but in seen from a larger prospective, it would make the world less safe for Norwegians if it becomes known that if one kidnaps a Norwegian one can expect a ransom,” he said.
Sekkingstad, Ridsdel, Hall and Flor, Hall's Filipina girlfriend, were abducted in 2015 from a resort on Samal island, hundreds of kilometres from Abu Sayyaf's traditional strongholds.
Although its leaders have pledged fealty to Isis, analysts say they are more focused on lucrative kidnappings-for-ransom than on setting up a caliphate.
The group is believed to have just a few hundred militants but has been blamed for the worst terror attacks in Philippine history. Abu Sayyaf has withstood repeated US-backed military offensives, surviving by using the mountainous, jungle terrain of the southern islands to its advantage.
The Abu Sayyaf are also believed to be holding four Malaysians, a Dutch bird-watcher and four Filipinos, seized in separate raids.