The RNLI said it sent its all-weather Lochinver lifeboat out at 9.42pm on Tuesday after the boat failed to return, and Police Scotland were later notified of its disappearance at 11.35pm the same night.
HM Coastguard has previously said an aircraft, two helicopters, six rescue teams and a local vessel were involved in the search.
Police understand the Kilda left the Brevaig area in the west of the island at about 7.30am on Tuesday, before travelling to the Port of Ness area to work.
After an extensive search, HM Coastguard said on Thursday evening that the response has been stood down, pending any new information.
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