The bank has seen a "high level" of crypto investment scams, a company spokesman said.
BBVA said the service will be available only to clients in Switzerland because of the country's clear regulations and the widespread adoption of digital assets.
Smaller countries such as Greece, Latvia, Lithuania and Estonia would be hit the hardest.
Lempres takes over from Dennis Frank, who had served as chairman since 1996.
The temporary ban was in response to concern about "high levels of suspected financial crime” associated with such payments.
Karatbars, issuer of a purportedly gold-backed crypto token, is under investigation by Florida regulators over links to a Miami “crypto bank.”
The bank plans to make it even harder to create anonymous crypto exchange accounts in South Korea.
A pilot test was successfully conducted for a Spanish-backed blockchain project to increase the efficiency of registering issuances.
A person with knowledge of the situation said all major banks are likely to be weighing the same decision.
An Idaho resident has sued the bank on behalf of "hundreds or thousands" of affected cryptocurrency investors.