The killing has shocked the Netherlands
The Dutch Government has announced next week's general election will go ahead as planned, despite Fortuyn's murder on Monday evening.
Police say they have detained their prime suspect in the case - a 32-year-old white Dutchman.
Reports say he was an animal-rights activist angered by Fortuyn's calls to lift a ban on fur farming.
The public prosecutor said ammunition was found at the suspect's house, matching the calibre of the bullets which killed Fortuyn. Police also removed environmental literature from his home.
Fortuyn, 54, an openly gay politician who was attracting widespread support for his policy of restricting immigration to the Netherlands, was shot dead outside a radio station by a lone gunman.
Election go-ahead
Rotterdam was Fortuyn's home and political base, and crowds there marched and chanted in protest at the killing, which has shocked the country.
Prime Minister Wim Kok met political leaders on Tuesday - including members of Fortuyn's right-wing party - before announcing that there would be no postponement of the 15 May poll.
"It would be sensible not to change the original date," Mr Kok told reporters, adding that the decision meant that "democracy had prevailed".
During Tuesday's meeting with Mr Kok, Fortuyn's party - Fortuyn's List - requested that the election be held as originally planned.
"Of course we took into serious consideration what we heard from Pim Fortuyn's List, but also the opinions of the other political parties," Mr Kok said.
Sympathy vote
The BBC's Tim Franks says that some of Fortuyn's supporters are keen to press ahead with the poll, believing they will never have a better chance of winning support for a radical anti-immigration manifesto.
It is not clear yet whether the party will retain the name of its late leader. A new leader is due to be chosen after the elections.
Minutes after making the election announcement, the Dutch prime minister led a minute's silence in the upper house of Parliament in memory of Fortuyn.
"A dark shadow has fallen over the Netherlands that has given way to deep emotions," he told the house.
The murder has also caused consternation across Europe, with leaders expressing horror that such violence could erupt on the Dutch political scene.
'Close the borders'
Fortuyn came to prominence in March when his party made a strong showing in local elections in Rotterdam.
He provoked public indignation by calling for the Netherlands' borders to be closed to immigrants and by describing Islam as a "backward" religion.
Eyewitnesses said a single gunman shot Fortuyn as he got into a chauffeur-driven limousine in a media park after a radio interview in the city of Hilversum, near Amsterdam.
He was hit six times, suffering multiple wounds in the head, chest and neck, and died shortly afterwards.
In an interview last week, Fortuyn expressed fears that he might be the victim of an attack and said he had received threats by phone, email and letter.