Finnish Foreign Minister Erkki Tuomioja held talks in Sanaa on Sunday on the fate of a couple from Finland held hostage in Yemen together with an Austrian since December.
State media said he met President Abdrabuh Mansur Hadi, who did not rule out the use of force to secure their release.
"The hostages must be released using all means possible, including the use of force, but with caution to make sure they remain safe," said Hadi, quoted on the defence ministry's website.
The three Europeans were abducted in the Yemeni capital on December 21 as they prepared to travel to the southern port of Aden.
In early January, Yemeni security officials said the Europeans were being held by Al Qaeda-linked tribesmen in Marib province of eastern Yemen.
Yemeni forces in January suspended an offensive aimed at freeing the hostages that cost more than 65 lives, and tribal mediators were allowed to attempt a negotiation with the kidnappers.
Most kidnappings of foreigners are carried out by members of Yemen'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 militants, active in the south and east of Yemen, rarely carry out kidnappings, but a Saudi diplomat, Abdullah al-Khalidi, has remained in the hands of the jihadist network since his abduction in Aden on March 28, 2012.