WASHINGTON — In repeating his readiness to pursue a new nuclear deal with Iran, President Trump this week left unmentioned his administration’s aim to hobble what officials call Tehran’s “expansionist foreign policy” — an ambitious priority that is far more likely to lead the United States into war.

The expansive, open-ended mission of wrestling with Iran’s diplomacy and military activity could prompt armed conflict well before any showdown over a nuclear program, according to lawmakers, former government officials and analysts.

The rising tensions between the United States and Iran this month have been fueled by American suspicions of Iranian military activity. And there is no sign that Iranian leaders, who proudly regard their nation as a major international player and a successor of Persian empires, will curb their attempts to exert influence across the Middle East.

On Wednesday, John R. Bolton, the White House national security adviser, asserted without presenting evidence that naval mines “almost certainly from Iran” caused recent explosions at four oil tankers in the Persian Gulf.