The decision was made after animal health investigators were unable to rule out the presence of H5N8 avian flu at a third farm in Wyre.
They said a "pro-active culling" would take place of birds including pheasants, partridges and ducks.
The Food Standards Agency said the disease was not a risk to food safety.
Public Health England said the risk to public health from the virus was very low.
The first outbreak was discovered last week at a farm in Wyre with 10,000 birds, followed by a second case involving a flock of about 1,000 birds.
Defra said the third premises would be cleansed and disinfected, "further reducing the risk that disease can be spread to other birds".
"Our investigations will continue and the restrictions already placed on the sites will remain in force until cleansing and disinfection is finished and the investigation is complete," a spokesperson said.
In January, there have been a number of other outbreaks of the virus, including at farms in Lincolnshire, North Yorkshire and in Carmarthenshire.

Deaf and blind people face a situation that is "still grim", according to charities Action on Hearing Loss Cymru, RNIB Cymru and Sense Cymru.
New standards were introduced by the Welsh government over a year ago aimed at ensuring equal access to healthcare.
But the report says little progress has been made.
Richard Williams, director of Action on Hearing Loss Cymru said the charities that authored the report are "really concerned" that people are leaving surgeries and hospitals unclear about what doctors have told them, what medication they need or whether operations have been successful.
New standards were brought in after a BBC Wales investigation in 2013 found health boards were breaching equality laws by not providing accessible services for the deaf and hard of hearing.
But 91 per cent of people surveyed for the report said they were not aware of improvements in the way healthcare providers communicate and share information with them.
Kay Coleman from Swansea began losing her hearing 15 years ago and said she finds it "incredibly difficult" to book a doctor's appointment.
An estimated 500,000 people are affected by hearing loss and 100,000 are living with sight loss in Wales.
In a statement the Welsh government said it is "committed to ensuring the standards are fully implemented" and it is working with relevant bodies "to establish how best to capture and record communication preferences for those with sensory loss to ensure their needs are fully met in every healthcare setting".

England won the toss and chose to bat but went from 110-2 to 184 all out as they were dismissed in 40.2 overs.
Daniel Bell-Drummond top-scored with 51 but it was in vain as England went 3-0 down in the five-match series.
Sri Lanka A reached their target in 37 overs as Shehan Jayasuriya followed up his 5-35 with a knock of 83.
About 63,000 birds are due to be culled at a Lancashire farm to prevent the spread of bird flu, which has already been found at two nearby premises.
[NEXT_CONCEPT]
The 600,000 people in Wales living with sensory loss are not having their basic healthcare needs met, according to a new report.
[NEXT_CONCEPT]
England Lions have lost their one-day series against Sri Lanka A after being beaten by four wickets in the third ODI in Kurunegala.