Britain backs the deployment of a European force to Somalia
The UK will not pay ransom to pirates because it would only encourage further hostage-taking, Foreign Secretary David Miliband has said.
Some reports say Somali pirates who hijacked a Saudi oil tanker have demanded $25m (£17m) to release the 25 hostages on board.
Britons Peter French, from County Durham, and James Grady, from the Strathclyde area, are among them.
Mr Miliband said he was "extremely concerned" and urged a "firm stand".
He said: "There is a strong view of the British Government, and actually the international community, that payments for hostage-taking are only an encouragement to further hostage-taking.
"We will be approaching this issue in a very delicate way, in a way that puts the security and safety of the hostages to the fore."
Mr French is the chief engineer and Mr Grady the second officer on the Sirius Star, which is anchored off the coast of Somalia, east Africa.
Their families said they hoped the men would be "home safely very soon".
The Saudi-owned ship was carrying two million barrels of oil worth more than $100m (£67m) when it was attacked on Saturday.
The AFP news agency, quoting one of the pirates, said the vessel's owners have been set a 10-day deadline to hand over the money.
But the ship's owners, Dubai-based Vela International Marine, have since cast doubt on that account.
Mr Miliband said the planned deployment of a European force to the region was the right course of action.
"It is very important that the international community stands firm against the scourge of hostage-taking, whether it is on boats... airlines, or elsewhere," he said.
"All of our hearts go out to all of those people who are now hostages on that ship, obviously in our case especially for the two British hostages.
"Their families will be going through a wrenching hell of waiting. It is important we assure them we are fully engaged with all of our partners on this issue."
The Sirius Star is the largest vessel ever to be hijacked in the area.
The pirates boarded it more than 400 nautical miles from the Kenyan port of Mombasa.
More than 90 vessels have come under attack this year off the coast of Somalia.