Thousands also marched in other Spanish cities, but the Valencia regional authorities put the turnout in the regional capital at 130,000.
Some protesters shouted "Murderers! Murderers!" and some carried placards denouncing Valencia's regional president as well as Spanish Prime Minister Pedro Sanchez.
The region was the worst hit by last month's floods, the most serious in decades, which killed at least 220 people and left towns and cities swamped with mud.
Local people are furious about the lack of warning, some pointing out that official alerts for the floods landed on people's phones when cars were already being washed away.
There is anger too over what critics say was the slow response of the authorities in the aftermath of the deadly flash floods that affected around 80 towns and cities in the region.
Police and protesters faced off on Saturday in a tense atmosphere, with some clashes breaking out, an AFP journalist witnessed.
The rally started in the square in front of city hall before a march to the Valencia regional headquarters.
Some protesters had harsh words for regional president Carlos Mazon, a 50-year-old lawyer who is a member of the right-wing opposition Popular Party.
Mazon was among the senior figures pelted with mud by angry protesters last Sunday -- along with Felipe VI and Queen Letizia of Spain -- as they visited the flood-hit region.
"Mazon's management has been outrageous and he should resign," 75-year-old Julian Garcia told AFP.
"In the hours before, they should have warned people to be on the alert, not to take their children to school, not to take their cars to work," he added.
But while the Valencia regional government was too slow to ask for help from Madrid, the central government also shared some of the blame, said Garcia.
As beleaguered residents waited for official help to arrive, many local people took matters into their own hands, turning out in large numbers to start the clean-up themselves.
Some of the marchers chanted what has become a popular refrain in recent weeks: "Solo el pueblo salva el pueblo!" (Only the people save the people).
- 'Shameful' -
Of the 220 deaths confirmed so far, 212 of them were killed in the Valencia region. The clean-up operations in some villages -- and the search for bodies of dozens of missing people -- is still going on.
Ana de la Rosa, a 30-year-old archivist, blamed poor management and political in-fighting between the regional and national authorities.
"They got mixed up in political guerilla warfare when it wasn't the time," she said.
De la Rosa argued that it was not enough for the key officials to resign: there was a case to be made that their mismanagement amounted to manslaughter, she said.
Another demonstrator, 50-year-old Trini Orduna, said that both the regional and national authorities should take their share of the blame, describing the country's political class as "shameful".
Protesters also marched in other cities across Spain, including Madrid and Alicante, in the Valencia region.
The health board of the Valencia region has reported no outbreaks of infectious diseases or a major threat to public health.
Even so, regional health authorities have asked local councils to apply measures to control and prevent the proliferation of mosquitoes and other insects capable of spreading diseases.
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