Despite the threats, Pegida plans to continue in Dresden in the future.
"We will not let them take away our right to gather or our freedom of expression," said Oertel at a press conference on Monday.
On Sunday, the group, which stands for Patriotic Europeans Against the Islamisation of the West wrote on their Facebook page: "Cancelled! Dear friends, unfortunately we must cancel our 13th meeting due to security concerns.
"What in police jargon is called an 'abstract threat' has changed to a 'concrete death threat' against a member of the organising team. IS terrorists have ordered his assassination."
Dresden police said Sunday they had received information from federal and state counterparts indicating a "concrete threat" against the right-wing populist group.
There had been calls for would-be "assassins to mingle among the protesters… and to murder an individual member of the organising team of the Pegida demonstrations", police said in a notice on the 24-hour ban.
This was consistent with "an Arabic-language tweet that called the Pegida demonstrations an enemy of Islam", it said.
Top-circulation daily Bild said online that the threat targeted Pegida's most prominent organiser Lutz Bachmann.
A Pegida spokeswoman, Kathrin Oertel, confirmed on German television that Bachmann was the target.
Oertel had already said in an earlier statement it would have been "irresponsible to expose our sympathisers and our city to incalculable risks".
The Pegida marches, which have voiced anger against Islam and "criminal asylum seekers" and vented a host of other grievances began in Dresden in October with several hundred supporters and have since steadily grown.
They drew a record 25,000 people last Monday, in the wake of the attacks by radical Islamists in Paris in which 17 people were killed.
Also last Monday, some 100,000 Germans marched in nationwide counter-demonstrations against Pegida.
Dresden police said that after the latest information "and given the characteristics of terrorist attacks, we must assume the use of homicidal means and an immediate threat to life and limb of all participants of the demonstrations".
Because there were no individual suspects, Dresden police said it saw no alternative to the temporary suspension of the constitutional right to free assembly within city limits.
'Concrete death threat'
Pegida earlier told its followers on Facebook that its 13th planned rally had been scrapped, citing a threat from the Islamic State jihadist group, and portraying the cancellation as its own decision.
"What in police jargon is called an 'abstract threat' has changed to a 'concrete death threat' against a member of the organising team. Isis terrorists have ordered his assassination," it said in a statement.
It had decided to call off the Dresden event as it could not guarantee the security of marchers and feared "collateral damage".
Der Spiegel news weekly reported Friday that foreign intelligence services had picked up communications by some "known international jihadists" indicating they had discussed possible attacks on Pegida rallies.
"We take these leads very seriously," Spiegel quoted an unnamed high-ranking security official as saying.
Chancellor Angela Merkel last Thursday vowed to step up security measures against Islamist militants, while vowing that Germany would not be divided by extremism of any kind.
"Hate preachers, violent delinquents who act in the name of Islam, those behind them, and the intellectual arsonists of international terrorism will be rigorously fought with all legal means at the disposal of the state," she told parliament.
Merkel has also stressed that "Islam is part of Germany", vowed to defend Muslims against racist slurs and attacks, and charged that Pegida's leaders are motivated by "prejudice, coldness, even hatred in their hearts".
On Friday, around 250 police raided 11 premises linked to Islamists in Berlin, arresting two men of Turkish origin suspected of planning violence in Syria.
One of the men was suspected of "leading an Islamist extremist group made up of Turkish and Russian nationals from Chechnya and Dagestan," police said.
Germany's internal security service has placed around 100 Islamist groups, each comprising 10 to 80 people, under observation since last year, another news report said Sunday.
The surveillance targets included Muslim prayer groups, online propagandists, people collecting donations for jihadists and fighters who had returned from the Middle East.
SEE ALSO: The rise and spread of Pegida