This would have required eBooks to become 50 per cent of all library lending within 10 years - something that has not been achieved at any library in the world.
Projections for the 2014/15 year had eBooks as 1.17 per cent of total issues within the city libraries.
Mr Crosby said he supported increasing the funding because, in the 1990s, book stock was reduced and "significant investment" was later needed to bring stock back to suitable levels.
"Driving book stock into the ground like in this recommendation will not work. We'll find ourselves in 2016/17/18 making substantial investment into book stock.
"The eBook is a red herring in my view," said Mr Crosby.
Cutting library stock would be a bad look when the new and improved Greerton Library opened and the council "can't fill the shelves with half reasonable books", he said.
Councillor Rich Curach said he could not support the resolution as pouring money into print books when there was a "clear transition into digital reading" was not a wise investment.
"It seems archaic to continue down this track with more print books."
Councillor Kelvin Clout said the mayor had made a sensible recommendation and he would be surprised if the review of library services came back with a recommendation of a $798,000 stock budget.
Councillor Gail McIntosh said allocating more money to giving Community Service Card holders free computer access would be a better investment.
Tauranga City libraries manager Jill Best said in America, libraries had eBooks for longer than in New Zealand and there, uptake was at about 30 per cent.
"It's looking now that eBooks are not going to take over the world, they will run in parallel with print books.
"Just like years ago when people thought televisions would take over books, they instead ran in parallel," she said.
"Most of the people who read eBooks read print books as well."
