LONDON—U.S. Secretary of State John Kerry met with heads of some of Europe’s biggest banks in London on Thursday to address their concerns about doing business in Iran, in a controversial push to ensure that Tehran sees the relief that the U.S. and other world powers pledged it in a nuclear accord that took effect in January.

After a roughly hourlong meeting, Mr. Kerry said he hoped to glean from bankers the obstacles they see to doing business with Iran and to address them.

...