SEOUL (Reuters) - South Korea's worst outbreak of bird fluhas spread to the capital with agriculture ministry officialssaying on Tuesday four dead birds raised at a Seoul districtgovernment office had tested positive.

South Korea has confirmed 24 cases of the deadly H5N1strain in poultry in about a month. It has killed more than 5million chickens and ducks but that has not stopped the virusfrom spreading at its fastest rate since the country reportedits first case in 2003.

The four birds were among 57 chickens, ducks and turkeysraised in pens at the district office in the eastern part ofSeoul. The ministry said it would take about a day to confirmif the dead birds had contracted the H5N1 strain.

The city had culled all the birds at the site and waslimiting access to a nearby zoo and livestock market, theministry said.

Most of the outbreaks have been concentrated in thesouthwest of the country.

South Korea had to kill 5.29 million birds during the firstoutbreak between late 2003 and early 2004. The second outbreakin 2006-2007 saw about half that number culled.

On Monday, North Korea said it was stepping up measures toprevent the outbreak from being carried over its borders bymigratory flocks.

The last known bird flu outbreak in impoverished NorthKorea was in 2005.

(Reporting by Lee Jiyeon and Jon Herskovitz; Editing byNick Macfie)