Barack Obama portrayed his plans for US military action in Syria as part of a broader strategy to topple Bashar al-Assad, as tougher White House rhetoric began to win over sceptical Republicans in Congress on Tuesday.

While stressing that Washington's primary goal remained "limited and proportional" attacks, to degrade Syria's chemical weapons capabilities and deter their future use, the president hinted at a broader long-term mission that may ultimately bring about a change of regime.

"It also fits into a broader strategy that can bring about over time the kind of strengthening of the opposition and the diplomatic, economic and political pressure required – so that ultimately we have a transition that can bring peace and stability, not only to Syria but to the region," he told senior members of Congress at a White House meeting on Tuesday.

Obama has long spoken of the US desire to see Assad step down, but this is the first time he has linked that policy objective to his threatened military strikes against Syria. It follows pressure on Monday, from senators John McCain and Lindsey Graham, to make such a goal more explicit.

The apparent change of emphasis appeared to resolve some of the political deadlock on Capitol Hill on Tuesday, as House speaker John Boehner and a series of other Republican leaders announced that they would back the president's call for military authorisation from Congress.

There was more good news for Obama when secretary of state John Kerry and defence secretary Chuck Hagel got a relatively easy ride when they testified later to the Senate foreign relations committee, convened in special session to discuss the issue of military authorisation.

The endorsement of GOP leaders could be important in winning over the Republican-controlled House, where Obama has failed to win any support since his re-election in November. But even the Republican leadership has struggled to control Tea Party radicals in the House, and an anti-interventionist wing in the Senate led by Rand Paul remains a substantial challenge for the White House.

"I'm going to support the president's call for action, and I believe my colleagues should support the president's call for action," Boehner said after meeting the president at the White House. "The use of these weapons has to be responded to, and only the United States has the capability and the capacity to stop Assad and to warn others around the world that this type of behaviour is not to be tolerated."

So far, the tougher US rhetoric does not seem to have deterred Democrats who back the president's call for military action on humanitarian grounds. Emerging from the White House meeting shortly after Boehner, House minority leader Nancy Pelosi said Syria's alleged used of chemical weapons was "outside the circle of acceptable human behaviour", but said she would not whip Democrats into voting yes.

"I don't think congressional authorisation is necessary, but I do think it is a good thing, and I think we can achieve it," she added.

For nearly three hours at a the Senate hearing later, the only voices speaking against intervention were those of anti-war campaigners who were repeatedly ejected from the hearing by security staff.

When senators Rand Paul and Tom Udall eventually began more hostile questioning of Kerry, he brushed it off by asking them to consider what Syria's response might be to a US decision not to strike. "I guarantee you there would be further chemical attacks," Kerry told Paul.

The administration also received crucial backing from the chairman of the joint chiefs of staff, General Martin Dempsey, who had recently been openly sceptical about the merits of US military intervention. Dempsey said the evidence of alleged Syrian chemical weapons use had changed his mind.

Chuck Hagel listens as John Kerry speaks to the Senate foreign relations committee. Photograph: Brendan Smialowski/AFP/Getty Images

But Kerry was forced to backtrack after appearing to acknowledge that US ground troops could become involved under certain scenarios.

"In the event that Syria imploded, for instance, or in the event there was a threat of a chemical weapons cache falling into the hands of al-Nusra or someone else, and it was clearly in the interests of our allies, all of us, the British, the French and others, to prevent those weapons of mass destruction [falling into their hands]," Kerry said, "I don't want to take off the table an option that might or might not be available to be available to the president."

Five times in subsequent exchanges, the secretary insisted he had not meant to imply that "boots on the ground" was something actively planned by the administration.

He also faced hostile questioning from McCain, who asked why the administration was not going further in helping Syrian rebels overthrow Assad.

The committee chairman, Bob Menendez, said he and other senior Democrats had not quite finished redrafting the proposed White House authorisation for military force, but hoped to do so in time for the committee to begin "marking it up", or voting on specific amendments, following a further classified briefing on Wednesday morning. Full votes before the Senate and House are expected early next week.

In his televised remarks earlier, Obama repeated the US's conclusion that Syria was responsible for chemical attacks on its own citizens. "We have high confidence that Syria used, in an indiscriminate fashion, chemical weapons that killed thousands of people," he said. "That poses a serious national security threat to the United States and to the region and, as a consequence, Assad and Syria needs to be held accountable."

With the chances of successful votes in Congress next week looking a little stronger, Obama will now head to Europe in the hope of persuading more world leaders to back his strategy. He arrives in Sweden on Wednesday for a short visit before attending the G20 international summit in St Petersburg, where he will face a frosty reception from his Russian hosts.

President François Hollande of France called on Europe's leaders to unite over Syria, but hopes in Washington that Britain might hold a fresh parliamentary vote over joining military action were dashed on Monday, when prime minister David Cameron ruled out such a move.

The White House first announced that it would provide limited military support to Syrian rebel groups in June, but it has been criticised for dragging its heels over fears that arms might fall into the wrong hands.

The alleged chemical attacks by Assad forces now seem to have strengthened the hands of those in Washington who favour more direct assistance. The New York Times reported on Tuesday that CIA-trained rebels were now operating inside Syria.