GOP Sens. John McCain John Sidney McCainKelly's lead widens to 10 points in Arizona Senate race: poll COVID response shows a way forward on private gun sale checks Trump pulls into must-win Arizona trailing in polls MORE (Ariz.) and Lindsey Graham Lindsey Olin GrahamSenate Republicans signal openness to working with Biden Loeffler calls for hearing in wake of Netflix's 'Cuties' Quinnipiac poll shows Graham, Harrison tied in South Carolina Senate race MORE (S.C.) are urging President Trump to step up U.S. military activity against Syrian President Bashar Assad in the wake of last week's airstrike.

"As part of a broader strategy, we urge the President to take greater military action to achieve our objectives, including grounding the Syrian air force and establishing safe havens inside Syria to protect Syrians," the two senators said in a joint statement on Tuesday.

They added that "there will never be a diplomatic solution as long as Assad dominates the battlefield."

Defense Secretary James Mattis signaled Tuesday that the airstrike was not an indication that the United States was preparing to ramp up its activities, while also warning Assad against carrying out a chemical attack similar to the one his administration launched last Tuesday.

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Mattis told reporters that Thursday's airstrike was in response to Syria breaking its 2013 pledge to remove its chemical weapons and a United Nations Security Council strategy that outlined the plan.

"The reason for the strike was that alone," he said. "It was not a harbinger of some change in our military campaign."

He added that the strike "was not a statement that we could enter full fledged, full bore into the most complex civil war probably raging on the planet at this time."

The Trump administration carried out an airstrike against an airbase in Syria last week in response to a chemical gas attack that U.S. officials and lawmakers have linked to Assad, according to The New York Times

GOP lawmakers have split over what they think Trump's next steps should be in Syria.

But Graham and McCain have vocally pressed the Trump administration to step up military activities aimed at Assad since late last week.

They added on Tuesday that the Trump administration needs to lay out a strategy that "secures U.S. and allied interests in Syria" including defeating the Islamic State in Iraq and Syria (ISIS) and ending the country's years-long civil war.