Iran’s leaders lashed out at Washington on Monday as the Trump administration raised economic sanctions to their maximum level, saying the latest punitive actions called for countermeasures to pressure the U.S. in return.

The acrimony pointed to a sharp elevation of tensions between Washington and Tehran as the Trump administration put into effect a ban on oil imported from Iran and listed more than 700 Iranian banks, companies and individuals under sanctions in the latest phase of a pressure campaign.

President...