WASHINGTON — With the humanitarian and refugee crisis in Syria spiraling to new depths, the Democratic and Republican vice-presidential candidates, in their debate on Tuesday, called for a more forceful American response to the civil war than President Obama has undertaken.

Even as they argued over Donald J. Trump’s income taxes and Hillary Clinton’s email practices, the candidates, Gov. Mike Pence of Indiana and Senator Tim Kaine of Virginia, found some common ground on what is perhaps the thorniest geopolitical crisis today.

Both said they favored a proposal to create humanitarian “safe zones” in northern Syria to protect civilians being bombarded by the Syrian government. Neither was precise about what would be needed to create such corridors, though analysts say it would almost certainly require American warplanes to enforce a no-fly zone.

Mr. Obama has steadfastly resisted such a step. Until this week, his administration was trying to negotiate a cease-fire with the Russians, who are helping Syrian government forces in their siege of Aleppo.