* Iran supports deal to cap oil output, offers ** action * API reports surprise drop in U.S. crude inventories * EIA supply report due later on Thursday (Updates prices, adds quotes, changes dateline from SINGAPORE) By Alex Lawler LONDON, Feb 18 (Reuters) - Oil rose towards $35 a barrel on Thursday after Iran welcomed plans by Russia and Saudi Arabia to freeze output and an industry report showed a surprise drop in U.S. inventories. The gain added to a more than 7 percent surge in the previous session, which came even though analysts said the market had overreacted to Iran's support for the caps and the Russian-Saudi move would **t likely reduce the global surplus. "It's a continuation of yesterday's move," said Carsten Fritsch, analyst at Commerzbank.