Ann Clwyd, MP for Cynon Valley and member of the select committee on international development, urged Asda shoppers to register concerns at local stores and ask for their views to be passed on to Asda's board.
The call follows a back-lash from anti-gun and environmental pressure groups following Wal-Mart's pounds 6.7bn takeover of Asda. Wal-Mart is the largest gun supplier in the US, where it sells them over the counter.
Ms Clwyd said: "A boycott would be one approach, but I would like to see a campaign to put pressure on them [Wal-Mart] to change their policy in the US. People could ask to see the manager in their local store and ask for their comments to be passed on. If enough people did it, it could have an effect."
Ms Clwyd said she would be registering her protest at the Asda branch in Cardiff where she occasionally shops. "I will be making my feelings known."
Asda said it would welcome comments. "We always welcome customer feedback. But we are trading as Asda, funded by the UK stores. This [the selling of guns] is very much a US issue, and the culture here in Britain is very different. It is very difficult to compare the two."
The head of the Gun Control Network, a UK pressure group set up after the Dunblane shootings, has questioned whether the UK "might be clasping a viper to our bosom by allowing Wal-Mart into this country". Gill Marshall- Andrews, the chairwoman, said: "I would not shop at Asda and I would not recommend anyone else did either."
Asda says it has no plans to sell any sort of firearms at its stores.