During his visit to the US, Khan had said that talking about curbs on press freedom in Pakistan was a "joke".
"It is clear that either you are very poorly informed, in which case you should urgently replace the people around you, or you are knowingly concealing the facts, which is very serious, given your responsibilities," RSF Secretary General Christophe Deloire wrote on Wednesday, reported Dawn newspaper.
The RSF alleged that it was an "obscenity" for Khan to say that press freedom was thriving in Pakistan.
Given a recent surge in press freedom violations, which the RSF enumerated in a statement, "you will appreciate that to talk of 'one of the freest presses in the world' is clearly tantamount to an obscenity," Deloire said.
He urged Khan to "allow Pakistan's journalists to exercise their profession in complete safety and with complete independence". The credibility of the Pakistani state and democracy is at stake, he said.
Earlier in July, the government launched a blistering attack on the press, linking critical coverage to potential "treason".
Also in July, a number of private television channels had their broadcasts cut after screening a press conference with former Prime Minister Nawaz Sharif's daughter Maryam Nawaz.
In recent years, the space for dissent has shrunk, with the government announcing a crackdown on social networks and traditional media houses decrying pressure from authorities that they say has resulted in widespread self-censorship.
( With inputs from IANS )