Environment Secretary Margaret Beckett said it would be "impracticable" to turn back two of the so-called "ghost ships" which are heading for the UK.
Four rusting US vessels are heading to UK shores
Four of the rusting former US navy ships are heading for Able UK's Hartlepool yard where they were due to be dismantled.
On Wednesday, the High Court blocked any work on dismantling the ships until legal challenges had been heard, following action by Friends of the Earth.
Mrs Beckett said following talks with US authorities it had been agreed the first two ships could not go back immediately, and talks were taking place about how they could be stored temporarily over the winter.
Two of the ships are due to anchor in Hartlepool on Wednesday.
But talks are continuing about a second pair of ships currently further away on their journey to UK shores.
In Thursday's statement from the Department for the Environment, Food and Rural
Affairs, Mrs Beckett said the Environment Agency had made clear the proposal to dismantle was inconsistent with international regulations.
"The government agrees that the law requires the ships to be returned to the US."
She said it would be preferable for the ships to be sent back, but added: "The government recognises that immediate return to the US of the first two ships, which are now approaching the Channel, would be impracticable."
She said US authorities had raised a number of reasons not to return the ships, in particular the weather.
Mrs Beckett said she had been working closely with the Environment Agency, US
authorities and Able UK, to achieve the best outcome.
She went on to say that facilities were available in the UK for dismantling the ships under robust regulation and played down the concerns of environmentalists.
In a statement on Thursday, Friends of the Earth said the ships should never have been allowed to set sail in the first place.
The campaign group demanded that the vessels did not come any further towards the
UK and should be temporarily housed at the first available port.
Oils and oily ballast water could cause damage to the marine environment.
Asbestos is a known carcinogen but is denser than water and non-soluable so would only pose a problem if blown on shore.
PCBs have been called a "probable carcinogen" and have been linked with neurological and developmental problems in humans.
Mercury, lead, chromium and cadmium are highly toxic metals which accumulate in the body.