This is largely a question of semantics.
The widest body of water in North America that is actually called a river is probably the Saint Lawrence. I measure the estuary at 133km at the upstream tip of Anticosti Island.
Further upstream on the same system, we have Lake Superior, the largest (Freshwater*) lake in the world by area. There is a peninsula on the southern shore which limits its width, but I measure it at 173km at the widest point. This is probably the widest body of fresh water in the world.
The gulf of California, if considered part of the Colorado River, would be wider. But that would not really count today, as a lot of the time the Colorado River does not reach the sea, because its entire flow is used for irrigation.
A more useful measure is the discharge, which is about 200000m3/s for the Amazon, and about a fifth of that for the next largest river by discharge. If we imagine a point on the Amazon of width 10km and average depth 20m, the average velocity would be 1 m/s. Some kind of definition by velocity would be useful to differentiate between rivers and lakes.
The two largest rivers in North America by discharge are the Saint Lawrence and the Mississippi, at around 17000m3/s each.
So far this has been a somewhat North America centric answer because I found the statistics there interesting, but now a shout out for my own continent: The Baltic Sea in Europe has a salinity of less than 1%, which by some stretch gives it a claim to being a "river." It is over 300km wide at its widest point, before it squeezes out into the Atlantic at Denmark.
*The Caspian sea, if you consider it a lake, is larger than Lake Superior. To me it is a sea, not a lake, as it is salty and has no outflow.