Mr Burnham said he wanted to draw up a code of practice
New laws against ticket touts have been ruled out, the government has said.
Instead, Culture Secretary Andy Burnham called for event organisers and promoters to agree to a voluntary code.
He said the practice of reselling tickets at inflated prices "leeches off" the nation's cultural life, but legislation should be a last resort.
But the auction website eBay said it was "sceptical" about the government's proposals, which it said would prevent ordinary fans selling spare briefs.
Mr Burnham was responding to a select committee report into secondary agents - popularly known as ticket touts.
He said that voluntary agreements could protect the "crown jewels" of British sport - Wimbledon tennis championships, world cups and major finals - by targeting sites such as eBay.
Ministers will work with the Society of Ticket Agents and Retailers (STAR) to draw up a new code of practice, which is likely to include a limit on the number of tickets sold per person.
"The re-selling of tickets at inflated prices doesn't add anything to the cultural life of the country, but instead leeches off it and denies access to those who are least able to afford tickets," Mr Burnham said.
"The days of turning up at the box office to buy tickets have been swept away by online ticket sales, but we have also seen a growth in the secondary market with tickets block-booked by people whose sole aim is to sell on at a profit.
"We will work with the industry to find a way to achieve this on a voluntary basis."
In response, a spokesman for eBay said the firm would study the government's proposals, but said that less than 1% of tickets for recent major sporting events were sold on the site.
"We are also sceptical about whether these proposals are workable, and note that the idea of a list of protected events has already been rejected by an all-party committee of MPs on the basis that it would simply add to confusion for consumers," he added.
But Geoff Huckstep of the National Arenas Association said he was "really not confident" that a voluntary code would go far enough and warned that secondary agents had previously "made a whole host of promises that they never kept".
"There already exists the legislation that they could extend," he told BBC Radio Five Live.
"So, for example, you cannot sell a Premiership football on a secondary site: eBay or the like. Why can't that be extended to concerts?"