Government believes current laws are enough to stop children buying unsuitable items online - if they are enforced properly.
Business minister Baroness Vadera has rejected calls for stronger regulation on internet shopping.
Labour's Baroness Massey of Darwen had argued that new legislation was required to force web retailers to ensure any products they sell which are unsuitable for children are not bought by minors. She wanted rules on internet gambling extended to retailers selling items like tobacco, alcohol and knives.
Lady Massey argued in the House of Lords that her Online Purchasing of Goods and Services (Age Verification) Bill would both protect children and ensure peace of mind for parents. However, Lady Vadera answered that there should be a stronger focus on enforcement of the current rules, as the law does not make a distinction between online and offline transactions.
Bringing in tighter age-verification controls on the internet has been backed by the Children's Charities Coalition on Internet Safety, which counts Barnardo's and Action for Children among its members.
"Retailers' increasingly successful efforts to control the sale of age restricted products over the counter on the high street are being seriously undermined by their failure to take similarly effective steps to limit sales of exactly the same items on the internet," Zoe Hilton, an NSPCC policy advisor speaking on behalf of the coalition, told the BBC.
