The ships were reportedly the Petrel 8, Hao Fan 6, Tong San 2 and Jie Shun.
The UN Security Council expanded sanctions on North Korea last month in response to Pyongyang's sixth and largest nuclear test yet.
The ban was announced following a UN meeting on Monday.
Mr Griffiths, speaking after the meeting on the enforcement of sanctions on North Korea, said the ships were found "transporting prohibited goods".
He said the ban, which went into effect on 5 October, did not entail asset freezes or travel bans.
According to the MarineTraffic website, a maritime database that monitors the movement of vessels, Petrel 8 is registered in Comoros, Hao Fan 6 in Saint Kitts and Nevis, and Tong San 2 in North Korea. The registered country of Jie Shun is not listed.
In August, a UN resolution banned exports of coal, seafood and iron ore from North Korea. Sanctions were expanded last month to include the export of textiles and North Korean guest workers, as well as a cap on oil imports.
The tightening of trade restrictions followed Pyongyang's sixth nuclear test and the firing of two missiles over Japan.
North Korea's main economic partner China has signed up to the measures, along with Russia. Both have previously vetoed harsher sanctions on the secretive state.
The export of coal, ore and other raw materials to China is one of North Korea's few sources of foreign cash. Estimates say that North Korea exports about $3bn worth of goods each year - and the sanctions could eliminate $1bn of that trade.
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