Writing in a Facebook post, Pegida said the cancellation of Monday's rally was a "sleight of hand" by the city's mayor.
"Now we want, together with you, to show on Wednesday, 21.01.2015, in Leipzig WHO is the People. We need everyone who loves our land and is not an extremist, racist or xenophobe," the group said.
The announcement came hours after Pegida called off its planned demonstration in the movement's home city of Dresden on Monday, citing security reasons. It said there had been a "concrete threat" to a member of Pegida's organizing team, according to German police, which prompted it to cancel the demonstration.
Pegida has staged a number of organized anti-islamization rallies in Germany. Similar protests have taken place in Austria, France and Switzerland.
Many German officials condemn the movement, with anti-Pegida demonstrations regularly held in Germany.
