Parliament speaker Irakli Kobakhidze told reporters the authorities would not take any "hasty decisions" but rather try to get its message across to the public, the civil.ge news site reports.
"False information is being spread, so we need to pay particular attention to informing the public, and then take the decision together," he said, adding that opponents of the cannabis bill had "misled" Georgians into thinking it meant all drug restrictions would simply be dropped.
The interior ministry confirmed earlier this month that it wanted to approve the cultivation of medical cannabis strictly for export, emphasising that the sale of marijuana in Georgia itself "will remain a criminal offence", IPN news agencyreported.
The row over the seemingly-innocuous bill blew up in the wake of a dramatic summer of protests over police drug raids that activists said targeted gay-friendly night clubs in the capital Tbilisi.
The libertarian New Political Centre Girchi party launched a legal challenge to the drugs laws on the back of the protests, and the Constitutional Court effectively decriminalised cannabis for personal use.
The government denied any anti-LGBT agenda, but for the Church and its allies the whole question of drugs is tied up with their opposition to gay rights.
Fr Andria Jaghmaidze, who often puts the Church point of view across to the media, told the BBC that "LGBT propaganda promotes a drastically liberalised drugs policy that contradicts Church teachings".
The news about the cannabis cultivation bill prompted expressions of concern by senior bishops, culminating in a forthright sermon on Sunday by Patriarch Ilia II, the head of the Orthodox Church.
"The authorities need to take responsibility for this matter. It should not be handed over to the private sector. If it is, it will be hard to control it, and drug addicts will start coming here from foreign countries to enjoy the freedom," he thundered.
Hundreds of church-goers then marched on Freedom Square in the centre of Tbilisi, and the government - ever-mindful of the summer rallies and earlier Church-led protests against liberal social policies - decided it was best to put the bill on hold.
The authorities have argued that they are doing just what the Patriarch ordered - namely taking responsibility - but the waters are further muddied by money.
Finance Minister Ivane Machavariani said Georgia could earn $384m (£296m) in the coming two to three years by tapping into the growing cannabis-export market. Ilia II addressed this point directly in his sermon, saying "What is the use of the economy if we lose our children?"
The Church has forced a pause, but the government is determined to pass the law sooner rather than later. Irakli Kobakhidze said the bill is "an urgent matter", and parliament will return to it next week.
Unfortunately for the government, arguments and protests are unlikely to go away. One thing the Church and civil libertarians agree on is that the marijuana export bill could be a gateway to the legal cultivation and sale of drugs at home.
"Marijuana is legal, and there should be legal ways of obtaining legal substances. Marijuana production should become a normal business," Zurab Japaridze of the New Political Centre Girchi told civil.ge.