Secretary of State Rex Tillerson said Thursday that “steps are underway” on an international coalition to pressure Bashar Assad from power, as President Trump was being briefed on military options for Syria – though what specific steps the U.S. and its allies might take in response to the latest deadly chemical weapons attack remained unclear.

America’s top diplomat addressed the Syria crisis a day after Trump declared in the Rose Garden that the chemical strike would not be tolerated. Tillerson pointedly said Russia should “consider carefully” its support for the Assad regime, while calling for an international effort to defeat ISIS in Syria, stabilize the country and ultimately work with partners through a political process that leads to Assad leaving power.

Asked if the U.S. would organize a coalition to remove Assad, Tillerson said: “Those steps are underway.”

“It's a serious matter, it requires a serious response,” Tillerson said, adding the recent attack “violates all previous U.N. resolutions, violates international norms and long-held agreements.”

Tillerson made his remarks in West Palm Beach, Fla., after welcoming China's President Xi Jinping for a two-day summit with Trump. En route to Florida, Trump also said the attack "shouldn’t be allowed to happen."

Asked if Assad should go, Trump said, "He's there, and I guess he's running things so something should happen."

The statements come amid discussions at senior levels of the Pentagon and White House about the next moves in Syria -- and reflect a newly aggressive stance, mere days after the Trump administration appeared ready to accept Assad as the country’s leader for the foreseeable future.

The Obama administration for years pursued a strategy similar to that outlined Thursday by Tillerson, to little success. Trump has not said whether he would go further than his predecessor in using military force.

In Florida, however, Trump was set to receive a briefing Friday from Defense Secretary Jim Mattis and National Security Adviser H.R. McMaster on military options that could be taken in retaliation for this week’s chemical weapons strike, Fox News has learned.

According to senior military officials, McMaster and Mattis traveled to Florida to attend meetings with Trump and visiting Chinese President Xi and planned to discuss possible military action Thursday afternoon.

“There has been a ton of traffic on this in the last 48 hours,” a source told Fox News, adding that the chemical weapons attack was among the issues addressed during Wednesday’s National Security Council meeting.

There are currently two U.S. Navy warships in the eastern Mediterranean -- the USS Ross and USS Porter -- which could be called upon to strike in Syria if requested, multiple defense officials told Fox News.

On Capitol Hill, Sen. John McCain, R-Ariz., said he spoke with Trump on Wednesday and that he confirmed plans “to consult with General McMaster and General Mattis and make a decision there.”

On Thursday, McCain and Sen. Lindsey Graham, R-S.C., issued a joint statement asserting that “the latest use of chemical weapons” by the government of Assad requires action, calling for Trump to take out Syria’s air force.

“The message from the United States must be that this will not stand. We must show that no foreign power can or will protect Assad now. He must pay a punitive cost for this horrific attack,” read the statement.

As many as 72 Syrians, including women and children, were killed in Tuesday’s attack. The Syrian military denied it used chemical weapons against civilians.

Although Graham contended Trump does not need to congressional approval to take action, others are urging a more cautious approach.

Sen. Bob Corker, the Republican chairman of the Foreign Relations Committee, told reporters he first wanted to know which military options were under consideration by the White House.

Fox News' Jennifer Griffin and Lucas Tomlinson and The Associated Press contributed to this report.