The bill, which must be approved by President Uhuru Kenyatta to become law, would lead to huge fines against journalists and media organisations that violate a code of conduct.
Kenyan media vocally opposed the bill after it was approved by lawmakers last month, with one newspaper headline reading “No Mr President!”.
Kenyatta subsequently promised to review the bill, promising not to “gag” journalists.
On Friday, Deputy PM Ruto told a gathering of African media leaders in the Ethiopian capital Addis Ababa that “our Parliament passed a bill that we admit is contentious.”
“The President of Kenya has undertaken to refer the bill back to parliament so that these matters can be ironed out,” he added.
He also said that “discussions are underway between various stakeholders – Executive, Parliament and the media – to resolve the contentious issues”.
In his address, Ruto heralded the role of a free press in Africa, saying “the relationship between government and media does not need to be adversarial”.
The bill would set up the new Communications and Multimedia Appeals Tribunal with the power to impose penalties of up to Sh20 million (173,000 euros, $234,000) on offenders and even bar journalists from working.
The bill would also herald strict controls on radio and television broadcasts, with stations obliged to ensure that 45 percent of programme content and advertising is locally-made.
US-based media watchdog Committee to Protect Journalists condemned the bill and called on Kenyatta to block it entirely.