The newspaper, citing US military sources, reported that the campaign may have raised al-Zarqawi's profile and overstated his importance.
The reports says the campaign - which includes television reports, newspaper articles and internet postings - aims to turn Iraqis against al-Zarqawi by playing on their perceived dislike of foreigners.
The campaign also included a deliberate leak to a New York Times journalist, although the US military denied that there was an attempt to manipulate the press, the Washington Post said.
The "US home audience" was also a specific target of the campaign, which has been running for two years, the report said.
Colonel Derek Harvey, a military intelligence officer quoted in the report, told fellow officers that "our own focus on Zarqawi has enlarged his caricature, if you will - made him more important than he really is".
"The long-term threat is not Zarqawi or religious extremists but these former regime types and their friends," Harvey said.
Harvey admitted that al-Zarqawi and foreign fighters remained a very small proportion of the Iraqi insurgency, the report said.
According to the report, the US military claimed that the campaign had been successful, noting that Iraqi insurgents had attacked al-Zarqawi's followers.
But an American military spokesman denied that the threat from al-Zarqawi had been deliberately overstated.
"Make no mistake, Zarqawi and Al-Qaeda in Iraq are real threats to the citizens, security and stability of Iraq," General Rick Lynch said.
"We continue to conduct aggressive operations to eliminate the threat they pose not only to Iraq, but also to the rest of the region."
Recent unconfirmed reports said al-Zarqawi had been demoted or replaced as political leader of the Iraqi insurgency.
Al-Zarqawi has recieved three death sentences in his native Jordan for his involvement in attacks there.
The US says he is reponsible for dozens of killings in Iraq and has placed a $25 million price on his head.