"We're calling (Russia and Iran) out," Haley told "State of the Union" anchor Jake Tapper. "But I don't think anything is off the table at this point. I think what you're going to see is strong leadership. You're going to continue to see the United States act when we need to act."
Haley's comments came after Senate Majority Leader Mitch McConnell told lawmakers he would look into stepping up sanctions on both countries, whose leadership supports Syrian President Bashar al-Assad, who US officials say is responsible for a chemical weapons attack against civilians last week.
In response to that attack, President Donald Trump
ordered a US military strike against a Syrian air base
where the attack is thought to have originated.
But the Russians are denying that Assad had anything to do with the chemical attack. A spokesman for the Russian defense ministry said the US had no proof of chemical weapons at the air base.
Haley disagreed, telling Tapper that the US government has evidence.
"What we've seen is, you know, in our meetings this week, we were told of the evidence," she said. "We saw the evidence. The President saw the evidence. All of that is naturally classified. And I'm sure when they can declassify that, they will."
Haley also reiterated her warning
at the UN the day after the US strike.
"I was trying to give warning and notice to the members of the Security Council and the international community that (Trump) won't stop here," she said Sunday, adding. "If he needs to do more, he will do more."
Secretary of State Rex Tillerson, who is visiting Moscow this week to meet with his Russian counterparts, said Sunday he plans to ask them
about their commitment to ensuring Syria has no chemical weapons.
"Yes, that will part of the discussions when I visit Moscow next week is to call upon Foreign Minister (Sergey) Lavrov and the Russian government to fulfill the obligation it made to the international community when it agreed to be the guarantor of the elimination of the chemical weapons," he told ABC's George Stephanopoulos on "This Week." "And why Russia has not been able to achieve that is unclear to me. I don't draw conclusions of complicity at all, but clearly they've been incompetent and perhaps they've just simply been out-maneuvered by the Syrians."
Haley echoed his comments in somewhat harsher tones on "State of the Union." Asked whether she thought Russia was trying to help Assad cover up the use of chemical weapons, Haley said either Moscow knew Assad had weapons that would be used or they were "played for fools by Assad and kept in the dark."
"So they now have to answer for this," she said. "How can they with a straight face cover for Assad, because if they're covering for Assad, then what are they really saying? They're saying by covering for Assad that they knew that it was there, or they were incompetent by having chemical weapons there in the first place.
"There's a lot of answers that need to come from Russia," Haley said, adding that she thought some of those answers would come during Tillerson's meeting in Moscow.
Later on "State of the Union," Massachusetts Democratic Sen. Ed Markey rebuked Haley's call for regime change
, saying that would require a major military effort on the part of the US.
"When the Trump administration uses the words regime change, they are talking about a military effort to remove Assad," Markey told Tapper. "And that would mean putting American young men and women on the ground in battlefield conditions in order to accomplish that goal. I don't think there's any appetite in the United States for a massive additional military presence."
Trump's national security adviser, H.R. McMaster, said Sunday that he saw the situation as a "great opportunity" for Russia.
"Well this is part of the problem in Syria, is Russia's sponsorship of this murderous regime," McMaster said on "Fox News Sunday." "And so we would want to appeal rationally to Russia -- this is a great opportunity for the Russia leadership to re-evalute what they're doing. Why they're supporting a regime that commits mass murder against its own people."
Meanwhile, Syrian state media reported Sunday that Russia and Iran are drawing red lines after the US strike.
"We will respond strongly to any aggression on Syria," the two Syrian allies said in a joint statement that flashed in a banner on Syrian state television. "Russia and Iran will not allow America to dominate the world."
The Kremlin also issued a statement Sunday on Russian President Vladimir Putin and Iranian President Hassan Rouhani's discussion of the situation in Syria by phone. They said the US actions against a sovereign state violatied international law and called for an objective, unbiased investigation of all the circumstances of the chemical weapons incident, the statement said.
Syria has resumed operations
from the base since the attack, CNN has reported
. Speaking on "Meet the Press" on Sunday, South Carolina Republican Sen. Lindsey Graham didn't mince words about the message Assad might be sending.
"Here's what I think Assad's telling Trump by flying from this base: 'FU,'" Graham said.
Graham called that a "serious mistake."
"[I]f you're an adversary of the United States, and you don't worry about what Trump may do on any given day, then you're crazy," he said.