Cllr Adam McVey was shot down on social media by fellow SNP member Fiona Hyslop over his ambition for the policy within 12 months.
Any Transient Visitor Levy (TVL) would need the approval of the Scottish Government.
Posting on Twitter, Cllr McVey said: “In the next 12 months, our plans for a ‘tourist tax’ will be ready for implementation.
“While it may take longer to deliver the powers necessary to start collection, our timeline is robust and we will be ready to go.”
Ms Hyslop, who is currently on a trip to Japan, replied: “? ? ? So let’s be clear – you have no shared plans, no tourist business consultation and no agreement with Scottish Gov.”
The council is proposing adding £1 to hotel bills in order to drum up an estimated £11 million of extra revenue for the city.
Cllr McVey said: “All 32 local authority leaders now stand with Edinburgh and other councils looking to pursue a tourist tax and momentum is building.
“Key hotel industry leaders in the city are also joining the conversation and giving their support to our efforts. This is a key part of our programme for the Capital and I’m confident we will deliver a TVL in the best interests of our tourist economy and the people of Edinburgh.
“The Tories were the only party to oppose this policy in the Capital and while some agree with their stance, it is widely out of step with public opinion and the best interests of Edinburgh.”
While many believe the tax would generate much-needed funding for the city, opponents say the added charge could put pressure on businesses. Edinburgh Conservative group chairman, Cllr Jason Rust, said: “The proposals being brought forward by the SNP-led administration seem to be in absolute chaos to the extent they don’t have the confidence of their own Cabinet Secretary and are publicly split on this issue.
“It’s an embarrassment and really concerning if the council leader is making statements which are then ridiculed at government level. This leaves in tatters the oft repeated claim regarding the influence the council has with government.”
Scottish Labour’s communities spokesperson Monica Lennon said: “Our local communities are in serious need of additional funding, which means we need to urgently look at new ways for local authorities to raise revenues, including a tourist tax .