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WASHINGTON — Republican presidential candidate Carly Fiorina said Sunday the United States shouldn’t open its doors any wider to welcome Syrian refugees streaming into Europe.

The former technology executive, citing concerns about terrorism in explaining her position during an appearance on CBS’s ‘‘Face the Nation,’’ said the United States, ‘‘sadly, cannot relax our entrance criteria.’’

An estimated 4 million refugees have fled Syria since 2011. The United States has accepted about 1,000 Syrians this year among 70,000 refugees from across the world.

Some have called on the United States to expand its refugee program.

General Martin Dempsey, chairman of the Joint Chiefs of Staff, described the situation as ‘‘a shared responsibility among the civilized nation states of the world,’’ in an interview that aired Sunday on ABC’s ‘‘This Week.’’

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Yet Fiorina, a former Hewlett-Packard chief executive, said the United States should be ‘‘very careful about who we let enter this country from these war-torn regions to ensure that terrorists are not coming here.’’

Governor John Kasich of Ohio, another GOP presidential candidate, suggested there was room for the United States to play a bigger role.

‘‘I think we do have a responsibility in terms of taking some more folks in — making sure they assimilate, and at the same time, helping people to actually be safe as they move — that’s logistical support,’’ he told ABC. ‘‘But this is fundamentally an issue that Europe has to come to grips with.’’

The influx of immigrants entering the United States illegally has eased recently, but the political rhetoric is red-hot.

Donald Trump, the leading Republican presidential candidate, is calling for mass deportation of millions of immigrants living in the country without legal permission, and some of his rivals have joined in proposing to stop granting citizenship to children born to such immigrants and to wall off the US-Mexico border.

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