The non-English characters allow scammers to create “lookalike” sites with domain names almost indistinguishable from legitimate ones.
Farsight Security found scam sites posing as banks, loan advisers and children’s brands Lego and Haribo.
Smartphone users are at greater risk as small screens make lookalikes even harder to spot.
The Farsight Security report looked at more than 100 million domain names that use non-English character sets – introduced to make the net more familiar and usable for non-English speaking nations – and found about 27% of them had been created by scammers.
It also uncovered more than 8,000 separate characters that could be abused to confuse people.
Farsight founder Paul Vixie, who wrote much of the software underpinning the net’s domain names told the BBC: “Any lower case letter can be represented by as many as 40 different variations.”
And many internationalised versions added just a tiny fleck or mark that was not easy to see.
Eldar Tuvey, founder and head of security company Wandera, said it had also seen an upsurge in phishing domains using different ways of forming characters.
In particular, it had seen an almost doubling of the number of scam domains created using an encoding system called punycode over the past few months.
And phishing gangs were using messages sent via mobile apps to tempt people into clicking on the similar-looking links.
“They are targeting specific groups,” Mr Tuvey said.
And research had established people were three times more likely to fall for a phishing scam presented on their phone.
“To phish someone, you just have to fool them once,” Mr Tuvey said. “Tricking them into installing malware is much more work.”