The rains make it physically miserable for people living under makeshift tents, drenching them and knocking down their flimsy tents, our correspondent said.
They also raise fears of disease and flooding but washing human waste and rubbish scattered around the city into water catchment areas, potentially contaminating water supplies and clogging waterways, he added.
Hundreds of people marched on Thursday to the Port-au-Prince compound where the Haitian government has worked out of since its offices were devastated by the January 12 quake, before being blocked by riot police and United Nations forces.
"[The government] put some [tents] in the streets so that you can see them, but we haven't gotten any"
"We are out in the street since midnight. There is nowhere to sleep. They [the government] didn't give us any tents. They have put some in the streets so that you can see them, but we haven't gotten any, a demonstrator told the Associated Press news agency.
The UN says that out of the estimated one million displaced people on the streets of Haiti's capital, nearly 750,000 people have not received basic shelter like tents and plastic tarps, but there are fears that even the 250,000 who have received temporary or medium-term shelter remain vulnerable to the rainy season which starts around April.
Aid agencies say the top priority is to bring hazard resistant shelter which can withstand heavy rains and even hurricanes.
Americans may be freed
Meanwhile, the Haitian judge investigating the case of 10 Americans charged last week with child kidnapping and criminal association, said they should be released from jail while the probe continues.
Judge Bernard Saint-Vil on Thursday privately questioned the last of a group of parents who said they willingly gave their children to the five men and five women mostly from a Baptist church in the US state of Idaho, believing they would educate and care for them.
"After listening to the families, I see the possibility that they can all be released," Saint-Vil told the Associated Press. "I am recommending that all 10 Americans be released."
The judge has the final word on whether to free the Americans, although he has given the prosecutor-general the opportunity to raise objections.
It was unclear when the American might be released and the judge said it was too early to say whether they would be able to leave the country.