A survey of Welsh businesses and consumers suggests a majority of both support the nation getting its own domain name.
The move would offer website owners the chance to end their address with .wales and .cymru, instead of .uk.
Internet regulator ICANN will allow countries and other organisations to apply for the new names from January.
Supporters say it could help with branding, but critics warn it may increase the opportunity for fraud.
The poll was commissioned by the not-for-profit domain registry service Nominet. It suggests 69% of consumers backed the move and 59% of Welsh businesses and other bodies.
The poll used a sample of 1,003 individuals - 21% of whom were Welsh speakers - and 250 senior decision makers in Welsh organisations
However the survey suggested splits over which name to take.
"On the consumer side there was a slightly higher preference for .cymru," Nominet's director of business development, Glenn Hayward, told the BBC.
"Among businesses there was a much stronger preference for .wales to help them market themselves outside of the country."
Nominet suggests one solution would be for the both name to be registered. Website addresses ending in either suffix could then direct users to the same place.
However, ICANN is charging $185,000 (£116,045) per application and is refusing to let Wales be a special case.
The Welsh business minister, Edwina Hart, said last week that she is not considering paying for either application.
Nominet is in discussions to cover the costs and says it would set up a local office if its efforts succeed.
A spokesman said: "The findings demonstrate that there is a need to balance economic and linguistic considerations in making the decision between .cymru or .wales, and this on behalf of both those who speak Welsh and English".
However, a rival bidder, dotCYM, says giving Nominet control would amount to selling off the country's identity.
The London Economics Wales consultancy carried out the poll as part of a wider study.
"A Welsh domain name can play a positive supporting role in activities aimed at raising the brand profile of Wales and encouraging exports and inward investment," the report says.
"It can also provide a constant stream of low level but free advertising."
However the study also warns that such publicity comes at a price.
It says businesses and other brand owners will need to take defensive measures to prevent third parties operating sites with their name. They will also face additional marketing costs to publicise their new addresses.