The European Central Bank will follow up on its expected June interest rate cut with a gradual approach while keeping an eye out for any possible fallout from events in the Middle East, ECB policymaker Francois Villeroy de Galhau said on Tuesday.

"Barring major shocks and surprises, we should decide a first rate cut early June, followed by others in a pragmatic and agile gradualism," Villeroy said in a speech made in New York.

"And we will obviously monitor the possible consequences of the developments in the Middle East," he added.

(Reporting by Leigh Thomas; Editing by Sharon Singleton)