that Hurricane Dorian might hit Alabama, the New York Times reports.
It says this led to last week's statement by the agency, disavowing an earlier position by a regional office that the US state was not at risk.
The commerce department has dismissed the newspaper's report as "false".
Alabama was not hit by the storm.
Hurricane Dorian lashes US
Scale of Bahamas hurricane devastation emerges
Dorian had earlier battered the Bahamas, killing at least 30 people.
However, the local authorities have warned that the final death toll could be staggering.
What the row is all about?
In an Oval Office briefing last Wednesday, President Trump updated the US public about the approaching powerful storm, showing a forecast map by the National Oceanic and Atmospheric Administration (NOAA) from 29 August.
The map looked almost identical - but close observers soon spotted a difference.
The chart had a black loop marked around Alabama that was not on the original version.
White House spokesman Hogan Gidley later confirmed the map had been altered with a black felt-tip pen, known as a sharpie in the US, but did not say who made the edit.
Mr Trump earlier tweeted that several states, including Alabama, "will most likely be hit (much) harder than anticipated".
The NWS is part of the NAOO, which in turn is the branch of the commerce department.
Now the New York Times cites three people familiar with the issue as saying that last Friday Mr Ross had threatened to sack top NOAA employees unless they publicly backed Mr Trump's position.
The newspaper says that threat led to an unusual - unsigned - statement by the NOAA later on that day, saying that Hurricane Dorian "could impact Alabama".
The statement described the position by NWS's Birmingham office as "inconsistent with probabilities from the best forecast products available at the time".
Responding to the New York Times report, a spokesperson for the commerce department said: "The New York Times story is false".
"Secretary Ross did not threaten to fire any NOAA staff over forecasting and public statements about Hurricane Dorian," the spokesman added.
President Trump has so far not publicly commented over the latest developments.