More than 3,000 additional U.S. troops were headed for the Middle East on Monday to bolster defenses in case Iran makes good on its threat to retaliate for the Trump administration's targeted killing of a top general.

CBS News national security correspondent David Martin reported Monday that some U.S. military commanders had not been in favor of killing Iranian Major General Qassem Soleimani, on the grounds that Iran would feel compelled by its national honor to strike back, increasing the likelihood of a war nobody wants.

But the White House has stood by its decision to kill Soleimani in an airstrike last Friday, calling him a "terrorist" with the blood of hundreds of Americans on his hands and accusing him of plotting new attacks against U.S. personnel in the region. Mr. Trump personally is standing by his vow to target up to 52 significant sites inside Iran — including non-military cultural sites — should the Islamic Republic retaliate for the strike.

"They're allowed to kill our people and we're not allowed to touch their cultural sites? It doesn't work that way," he told reporters on Air Force One over the weekend.

Iran's foreign minister said Monday that any such attack would constitute a war crime.

In Tehran there was a huge funeral ceremony for Soleimani on Monday, marked by ever-escalating war rhetoric. CBS News correspondent Elizabeth Palmer said it has been three decades since crowds like the ones seen on Monday have turned out to mourn a leader in the Iranian capital, not since the death of previous Supreme Leader Ayatollah Khomeinei.

Soleimani was celebrated as a military commander, but in death he's being saluted as a hero, and a martyr. Iran's current Supreme Leader Ayatollah Khamenei wept as he led the prayer service in Tehran. He and Soleimani had worked closely together to steer Iran's foreign policy and extend its influence across the Middle East over recent years.

But Palmer said it was much more than a mourning procession. It was a political message; Iran was demonstrating that the country is united in grief — and rage at the United States.

Have you EVER seen such a sea of humanity in your life, @realdonaldtrump? Do you still want to listen to the clowns advising you on our region? And do you still imagine you can break the will of this great nation & its people? End of malign US presence in West Asia has begun. pic.twitter.com/5WzYM9OBuQ — Javad Zarif (@JZarif) January 6, 2020

Soleimani's daughter Zeinab addressed the crowd in Tehran on Monday, directly threatening an attack on U.S. military personnel in the Mideast. "The families of the American soldiers in western Asia... will spend their days waiting for the death of their children," she said as the crowd erupted in cheer.

In response to Mr. Trump's tweet threatening to strike Iranian cultural sites, Foreign Minister Jawad Zarif used his own Twitter account to denounce the U.S. leader's words as the threat of a war crime.

Palmer said lawmakers gathered in Iran's parliament on Monday chanted the now rote "Death to America" refrain, and leading politician Ali Larijani addressed the U.S. directly:

"You ought to know," he said, "that this deed will bring painful consequences."

It remained unclear Monday whether that means military reprisals by Tehran, but if so, they are likely to involve Hassan Nasrallah and his Hezbollah group. Hezbollah is Iran's proxy fighting force in Lebanon, and Nasrallah has warned that the U.S. will pay for killing Soliemani, though he said American citizens would not be targeted.

Iran has dozens of missiles at the ready, and between its domestic arsenal and its proxy forces like Hezbollah, even with America's military superiority and anti-missile systems it could unleash a barrage against U.S. forces based in Iraq. It could also target America's closest ally in the region, Israel, and has repeatedly threatened to do so.

As Martin reported, America is, for now, bracing for any Iranian retaliation with the deployment of the Immediate Response Force from the Army's 82nd Airborne division. The U.S. has more than enough firepower — both at sea and at air bases — to make good on Mr. Trump's threat to strike 52 targets in Iran.

But as the threats fly from both Tehran and Washington, former CIA Director and Middle East commander David Petraeus said Sunday on CBS' "Face the Nation" that the U.S. needs a plan to decrease tensions.

"There will there be a diplomatic initiative that says, 'okay, look, this is not headed in a good direction. We truly do want to de-escalate.' Everyone is going to lose if this continues to ratchet upward."

Susan Rice, who served as the U.S. national security adviser from 2013 to 2017, wrote in an opinion piece for The New York Times that while a full-scale conflict with Iran was not inevitable,"the probability is higher than at any point in decades."