I would say something like: The roads are flooded by heavy rain.
The roads are waterlogged .
(this usage might be Indian English-specific)
Most of the roads have been rendered impassable by heavy rain.
Examples from the media:
"Many roads remain impassable and are covered by water ."
( source ) "
Another day of downpours brought more water-covered roads .
Several roads in South Moorhead flooded Wednesday and Thursday
North Fargo got the brunt of it."
( source )
ell.stackexchange.com/users/2127/CowperKettle
Surface water is another word for rainwater – more specifically, rainwater that falls on the ground, on roofs and roads , pavements and paths.
As an example usage similar to OP's context, consider... I was forced to drive slowly due to the pools of surface water on the roads.
ell.stackexchange.com/users/126/FumbleFingers Reinstate Monica
(A slight deviation to @FumbleFingers' answer)
Standing water is quite possibly the term.
ell.stackexchange.com/users/18011/PCARR
There is really nothing that unnatural with your own words (which is often the case here; people tend to overthink things): Most of the roads on my route have accumulated rain water and it is raining heavily.
I might reverse the terms, because and can suggest a cause-and-effect relationship or a Step-1, Step-2 sequence:
It is raining heavily and (to my knowledge) most of the roads on my route have accumulated rain water.
If in the US, you could add:
According to the National Weather Service there are Flash Flood Warnings in the area.
And remind your client of the possible peril:
I really don't think it is safe for either you or me to risk driving over a low-lying area where there is water over the road
All the above are natural phrases for a telephone conversation.
Or just keep it simple:
It's raining hard and there's a lot of water on the roads (in my area).
[It's not safe to drive.]
ell.stackexchange.com/users/None/
A slightly alternative phrasing would be The roads are inundated and impassable.
ell.stackexchange.com/users/21298/WhatRoughBeast
Puddles, large or small forming everywhere on the road after a few showers is appropriate in the Indian context.
The puddles form not because of the rain being heavy or light but because of improper laying of the road.
ell.stackexchange.com/users/94788/D.Raja
I was making a phone conversation with one of my client. I had promised him to do a meeting at a certain place. But I wanted to cancel that meeting because most of the roads on my route had accumulated rain water and it was raining heavily. For that I used the phrase   'road are blocked because of heavy rains'   Can you let me know a key word that could describe the road condition.
Word for describing 'water accumulated on roads'
ell.stackexchange.com
<word-request>
ell.stackexchange.com/questions/62243
ell.stackexchange.com/users/15349/NewStackUser
"Standing water", "puddles", "inundated and impassable", "waterlogged" and "flooded" are all terms that can be used to describe conditions when water has accumulated on roads. Inundated, flooded, waterlogged, rendered impassable by heavy rain, puddles and standing water are options.
Inundated, flooded, waterlogged are options. Rendered impassable by heavy rain, puddles and standing water are options.