The firms building the Royal Navy's two new aircraft carriers say the cost has risen by at least £1bn and possibly almost £2bn, the BBC has learned.
This could push the final cost of HMS Queen Elizabeth and HMS Prince of Wales to about £7bn - from the agreed £5.2bn.
At least one of the carriers is to be redesigned to take the US Navy's version of the Joint Strike Fighter.
Defence Secretary Liam Fox said the government would take a "fairly stiff view" of any costs increase.
The Ministry of Defence said no final decisions on a redesign had been taken, but added that it believed the final cost of the 60,000-tonne vessels, to be based in Portsmouth, would be closer to £6bn than £7bn.
The ships - which are being built by the Aircraft Carrier Alliance, the members of which are BAE systems, Babcock and Thales - were saved from defence cuts under the coalition government because it would cost more to cancel the projects than proceed with them.
Ministers agreed to change the design of one, or both, of the aircraft carriers to make them compatible with different aircraft.
To take the US Navy's version of the Joint Strike Fighter, they will need to be fitted with catapults and traps - or "cats and traps" - rather than ramps.
Last November, the UK and France signed a defence treaty that agreed to share aircraft carrier resources, by keeping at least one vessel at sea between the two countries at any one time.
Each will be able to use the other's carrier in some form, certainly for training and possibly for operations.
Speaking at a Westminster lunch, Dr Fox accepted the government had increased the budget and time scale by introducing changes to the design to allow interoperability with US and French forces.
But he said: "What we are looking at is a capability that will last us, when we have it, for 50 years. Therefore it is essential to get the decisions right."
He added: "We will look at the contracting as we go through to the end of 2012 with a fairly stiff view."
HMS Prince of Wales will not enter service. It will be built but not kitted out, and then kept as a reserve vessel.
The government's strategic defence and security review in October 2010 outlined cuts of £4.7bn over four years.
The new carriers will replace the 22,000-tonne Invincible class aircraft carriers, HMS Invincible, HMS Illustrious and HMS Ark Royal.
HMS Invincible, mothballed in 2005, was put up for sale on a government internet auction website, while Ark Royal - the navy's flagship - was decommissioned in January and HMS Illustrious will be decommissioned in 2014.
Ark Royal was decommissioned ahead of schedule - along with RAF Harrier jump jets - meaning no planes will be able to fly from British aircraft carriers until 2019, when the HMS Queen Elizabeth is expected to enter service.
BBC business editor Robert Peston said: "The disclosure of the rise in costs is bound to reopen the debate about whether the UK really needs new carriers, especially since the UK will be without any aircraft carrier until 2019."