The vessel is known with the name "funnel beaker," a kind of ceramic which features a flat bottom with a funnel shaped neck.
Such earthenware is characteristic of the Funnel Beaker Culture (4000-2800 BC), which represents the first farmers in Scandinavia and the north European plain.
It was found in pieces in a former fjord east of Rodby Havn, on the south coast of Lolland, Denmark, Discovery News reported.
"It is one of three beakers at the site, which originally was deposited whole probably containing some food or liquid presumably as part of some long forgotten ritual," Line Marie Olesen, archaeologist at the Museum Lolland-Falster said.
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"It must have been left there while manufacturing the pot," Olesen said.
According to Olesen, a lot of time and symbolism was put into the manufacture and decoration of the funnel beakers and associated pots.
"From the contexts in which they appear it is obvious that they played an important part in everyday life, be it ritual or profane," she said.
"The fragile fingerprint, left unintentionally, is an anonymous, yet very personal signature, which somehow brings us a bit closer to the prehistoric people and their actions," Olesen added.