A big counter-demonstration is also being organised, similar in size.
Dresden is the birthplace of a movement called "Patriotic Europeans Against the Islamisation of the West" (Pegida), which staged a big rally a week ago.
Justice Minister Heiko Maas called Pegida's protests "a disgrace". But the Eurosceptic party AfD is sympathetic.
"Most of their demands are legitimate," said Bernd Lucke, leader of the conservative Alternativ fuer Deutschland (AfD), which has campaigned for a tougher policy on immigration, as well as rejection of the euro.
In the western city of Cologne, about 15,000 people attended a demonstration on Sunday to promote tolerance and open-mindedness, under the motto: "You are Cologne - no Nazis here."
Immigration has become a hot topic in Germany this year, amid a surge in the numbers of asylum seekers, fuelled by the wars in Syria and Iraq. Germany takes in more asylum seekers than any other country.
Germany expects 200,000 asylum claims for 2014, up from 127,000 in 2013.
|Lutz Bachmann launched the Pegida movement through a Facebook group|
The AfD leader in Dresden, Frauke Petry, said Pegida "is protesting against inadequate legislation on asylum rights - they are also demanding that German law be applied against law-breakers, and they are opposing religious extremism".
The centre-left Social Democrats (SPD) - in the ruling coalition with Chancellor Angela Merkel's Christian Democrats - called Pegida's organisers "Nazis in pinstripes".
Police sources, quoted by the Spiegel online news website, said hundreds of Pegida activists in Dresden were members of two hooligan groups regarded as far-right.
Minister Maas said Pegida must be "unmasked", and he called for a "broad counter-movement embracing civil society and all political parties".
Not sure what he means by 'unmasked', unless it is the fact that Bachmann spent 2 years in jail. Does a criminal conviction in the past make an organization criminal? Does it indicate that a man is racist?
The slur, 'Nazis in pinstripes' is absurd. There is no reasonable comparison between Nazi hatred for Jews and patriotic Germans who don't want Germany to become an Islamic state. The Jews never numbered more than several million in their history. Islam numbers about 1.5 billion. That number should be enough to scare the daylights out of you. A force that large moving in one direction is nearly unstoppable.
The 'Nazi' slur could only have been made by those who are either too blind, or too stupid, to read the very clear writing on the wall. They need to look at France, which is just waking up to the fact that France, as we know it, will disappear within two generations, and it is probably too late to do anything about it.
Creeping Islamisation will conquer all of Europe while our grandchildren are still alive, and it will do it with the complicity of astonishingly naive, liberal governments.