Tehran — Hours after President Trump said Iran appeared to be "standing down" after an intense week of soaring tension, a senior Iranian military commander vowed Thursday that there would be "harsher revenge" taken against the U.S. Mr. Trump indicated on Wednesday that he plans no further military response against Iran in a statement intended to lower tension in the Middle East.

But the general chosen to replace Qassem Soleimani, the top Iranian commander killed in a targeted strike on Mr. Trump's order last week, said Thursday morning that he would follow the same path as his predecessor.

Abdollah Araghi, a member of Iran's Joint Chiefs of Staff, said meanwhile that the country's powerful Revolutionary Guard would "impose a harsher revenge on the enemy in the near future," according to the country's state-run media.

The messages show that the U.S. can't afford to let its guard down, but they also highlight continued deep divisions inside Iranian society. Iran's political leaders said Wednesday that the Islamic Republic had "concluded" its response to America's targeted killing of a top Iranian general.

CBS News senior foreign correspondent Elizabeth Palmer says that while Iran's military commanders are vowing to fight on, with the goal of getting U.S. forces to leave the region, the headline in Tehran on Thursday was that — in the short term — the Americans aren't planning another military strike.

In the first real snowfall of the winter, residents of Iran's capital went about their business on Thursday feeling safer.

One resident, Caroline, told Palmer she had definitely been afraid of the prospect of an all-out war with the U.S. Like millions of others in Iran, she listened to President Trump's speech very closely.

She said she was relieved when he said there would not be any further American attack, and she "slept very well" after his remarks.

"The fact that we have this great military and equipment, however, does not mean we have to use it," Mr. Trump said Wednesday. "We do not want to use it."

On Iranian state-run TV, the president's decision not to strike back was framed as a climb-down by the U.S., and a win for Iran's Revolutionary Guards, who were able to showcase their missile arsenal with the strikes this week against Iraqi bases housing U.S. forces.

Those strikes were retaliation for the U.S. attack that killed Soleimani on Friday. His death brought millions of people into the streets of Iranian cities in a show of national unity, but the mourning masses didn't convey the whole story.

Just a few weeks ago, thousands of demonstrators were in the streets to vent their fury and frustration with their own government, for its corruption, ineptitude and repression.

But Palmer says the mood has changed completely since then, and for now the voices of dissent have gone quiet.