"I call on remaining states, the eight remaining states, to sign and ratify the treaty without further delay," Ban said in Vienna at an event marking the anniversary.
"Nuclear testing poisons water, causes cancers and pollutes the area with radioactive fallout for generations and generations to come," he said.
"We are here to honour the victims. The best tribute to them is action, to ban and to stop nuclear testing. Their sufferings should teach the world to end this madness."
It has been signed by 183 states and ratified by 164 including Russia, France and Britain, three of the nine countries which have, or are thought to have, nuclear weapons.
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But to enter in force, the treaty needs 44 particular "nuclear technology holder" states to ratify it, eight of whom have yet to do so.
These eight include the other six in the nuclear club -- the United States, China, India, Pakistan, North Korea and Israel -- as well as Iran and Egypt.
US President Barack Obama said in a major speech on nuclear weapons in Prague in 2009, shortly after taking office, that he would "immediately and aggressively pursue US ratification".
Seven years later, with Obama leaving office in January 2017 and the opposition Republicans controlling both houses of Congress, the issue appears to have been put on on the back burner.