About 10,000 Sudanese marched through Khartoum to protest against the publication and called for a boycott of Danish produce.
Those at Wednesday's march, which started at Khartoum University, carried banners reading: "We all sacrifice our lives for the Prophet Muhammad" and "Cut Danish produce".
Danish newspapers said they reprinted one of the cartoons in support of free speech after three men were arrested in an alleged plot to kill the cartoonist.
Al-Bashir said: "We are capable of delivering the decisive response ... boycotting personalities and companies.
Ali al-Sadiq, a foreign ministry spokesman, said: "We will implement the president's decision. We will ban all Danes from entering Sudan."
He did not say if the decision included diplomats. Danish consulate officials in Khartoum were not available for comment.
Protests and rioting started in 2006 in several Muslim countries when the cartoons, one showing the prophet with a turban resembling a bomb, appeared in a Danish daily.
At least 50 people were killed and three Danish embassies were attacked.
Protesters at Wednesday's rally chanted slogans against the US and Israel for what they said was conspiring to push Danish newspapers to reprint the cartoon.
|About 10,000 Sudanese marched through |
Khartoum to protest the publication [AFP]
Al-Bashir spoke in support of Palestinians and called for the liberation of Jerusalem.
He also warned of "other measures" against Denmark, but did not elaborate.
Abdul Halim al-Mutaafi, the governor of Khartoum, told the local Al Riyadiah radio station from the rally that the gathering would call for cutting relations with Denmark and pledged the Sudanese would boycott all Danish goods.
"We don't want them to come to our land nor will we like to go to their land," al-Mutaafi said.
Danish exports, mainly dairy products, to Sudan are minimal, unlike to other Muslim markets such as Saudi Arabia and Indonesia.
Several Danish aid groups operate in Sudan - which is one of the largest recipients of Danish aid - including the Danish Refugee Council and the Danish Red Cross, which runs large projects to alleviate human suffering in the western Darfur region.
The African country received $26m in aid from Denmark in 2006 and a $100m humanitarian and reconstruction package is planned until the end of 2009.