The trio were abducted in Sanaa on December 21 by tribesmen with grievances over land seized from them in the capital and were initially held in Khawlan, a mountainous area 80 kilometres southeast of Sanaa.
AFP quotes a tribal source as saying that the kidnappers have widened their demands, calling for a ransom and the release of Al-Qaeda leaders jailed in Sanaa.
Ambassador meets with interior minister
On Wednesday, Interior Minister Abdelqader Qahtan received envoy Jarno Syrjälä, the Finnish Ambassador to Saudi Arabia. Finland does not have a diplomatic representation in Yemen, but the embassy in Riyadh is also responsible for ties with Yemen, Oman and Kuwait.
The minister assured Syrjälä that "efforts are ongoing to free the hostages without endangering their lives," according to state news agency Saba.
The Austrian man and the Finnish couple were abducted as they prepared to travel to the southern port of Aden via second city Ta’izz. The men were in the country studying Arabic, and the woman had just arrived for a visit.
On Wednesday Yemeni media reported that the trio had been handed over to al-Qaeda elements for a payment of some 21,000 euros, and were being held at al-Baida in southern Yemen. The Finnish Foreign Ministry declined to comment on the report.
Most kidnappings of foreigners are carried out by members of the country's powerful tribes who use them as bargaining chips in disputes with the central government.Hundreds of people have been abducted in Yemen over the past 15 years. Almost all have been freed unharmed.
Al-Qaeda took advantage of the weakness of Yemen's central government during an uprising in 2011 against now ousted president Ali Abdullah Saleh, seizing large swathes of territory across the south. But a month-long government offensive that ended in June pushed most of the militants to the more lawless desert regions of the east.