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"The goal of the movement of American ships is to strengthen the siege imposed on Yemen and put the Yemeni people under collective punishment," Houthi politburo member Mohammed al-Bukhaiti told Reuters. "This step increases the level of their participation in this war."
The United Nations Security Council imposed an arms embargo on Houthi leaders last week.
U.S. Fifth Fleet spokesman Kevin Stephens said there are a number of steps the Navy could take if it has indications that weapons are on Iranian ships, including a simple request to come aboard.
In addition to the USS Theodore Roosevelt and the USS Normandy, the U.S. has seven other U.S. battleships in the area, including the Iwo Jima Amphibious Ready Group, which includes a complement of more than 2,000 U.S. Marines. There are also three U.S. resupply ships in the region.
Iran, meanwhile, is calling for an immediate cease-fire in Yemen, where Houthi rebels have seized territory amid the Saudi-led campaign of airstrikes backing President Abd-Rabbu Mansour Hadi.
Iranian President Hassan Rouhani said Tuesday the proposal, which calls for a halt in fighting, talks among the Yemeni parties and formation of an inclusive government, is the way to solve the country's crisis.
Saudi Arabia says it is stopping its Arab coalition airstrikes on the Houthis in Yemen, but is not easing the pressure on the rebels.
Saudi officials said Tuesday after four weeks of bombings, the Houthis no longer pose a threat to Yemeni civilians or other countries, including Saudi Arabia.
U.S. defense officials said Tuesday that while some of the Saudi airstrikes had been very effective, they would welcome a cease-fire and are closely monitoring developments.
In other developments, the World Health Organization is warning of an imminent collapse in Yemen's health-care services, due to increasing shortages of critical medicines and health materials, disruptions in power supplies and a lack of fuel for generators.
The United Nations says more than 600 people have been killed and about 100,000 people have been displaced by the conflict in Yemen.