Hard-line groups in favor of reducing the number of immigrants entering the country are ripping President Trump Donald John TrumpBubba Wallace to be driver of Michael Jordan, Denny Hamlin NASCAR team Graham: GOP will confirm Trump's Supreme Court nominee before the election Southwest Airlines, unions call for six-month extension of government aid MORE's new executive order pausing the issuance of some green cards, arguing the measure falls far short of what his tweet earlier in the week promised.

The Federation for American Immigration Reform (FAIR) sent a letter to Trump on Thursday saying the executive order "does not deliver" and accused the president of "placating to business interests" by including exemptions for temporary workers.

"The American public understands that a meaningful pause of immigration must include all immigration, especially guestworkers," FAIR President Dan Stein wrote.

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The group called on Trump to issue a new executive order in the next 30 days that includes "all forms of immigration, including guest worker programs, which would allow hundreds of thousands of Americans out of the labor force to come back in, both now and when the economy finally starts to recover."

Trump set off a scramble late Monday when he tweeted that he would sign an executive order "to temporarily suspend immigration into the United States." The president cited skyrocketing unemployment due to the coronavirus in justifying the move, saying American workers should not have to compete with immigrants for jobs until the economy rebounds.

The order, signed Wednesday evening, suspends the issuance of green cards for 60 days for foreign nationals outside the United States seeking permanent residence. But it contains a number of exceptions.

Foreign nationals already in the U.S. who are applying for green cards are unaffected. Spouses and children of those already in the country with citizenship are also exempt, as are guest workers in the agriculture and technology industries and those considered part of the "national interest."

"We may modify it as we go along," Trump told reporters Wednesday, saying it could be "made tougher or made less tough."

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"We don't want to hurt our businesses, and we don't want to hurt our farmers," he added.

The various exceptions in the order have drawn criticism from groups that largely back Trump's push to curb legal and illegal immigration, a cornerstone of the president's first term. The administration has constructed a wall along portions of the southern border, imposed a policy that led to the separation of migrant families and implemented measures that restrict which foreigners can apply for asylum.

Several hard-line groups praised Trump for stating publicly in recent days that an influx of immigrants puts U.S. workers at a disadvantage. But they later expressed disappointment that the executive order did not match the president’s promise.

Roy Beck, head of NumbersUSA, lamented in a statement that "corporate lobbyists and other immigration expansionists in the White House persuaded the President to significantly water down" the executive order. He said it will ultimately fall to Congress to enact more expansive immigration reform.

The Center for Immigration Studies called the executive order "confusing" and argued it would have little tangible effect on Americans put out of work by the coronavirus pandemic. The group called for Trump to suspend "all temporary work visa programs" and scale back work permits for foreign students and spouses of temporary workers.

"There is no case for bringing in a million temporary visa workers when 22 million American workers are unemployed," Jessica Vaughan, director of policy studies at Center for Immigration Studies, said in a blog post reacting to the order.

There are still questions about how significant the impact will be, given the administration has already restricted travel from China, Europe, Mexico and Canada and closed consulates for most visa interviews during the global pandemic.

Democrats and immigrant advocacy groups have panned the executive order, even with its exemptions, accusing Trump of scapegoating immigrants and attempting to shift the focus away from criticism of his handling of the pandemic.

They have expressed additional concerns that the order remains open ended. Trump said it will be reviewed after 60 days, at which point he will determine whether to extend it based on economic conditions.

Experts and business leaders have warned that the economic rebound could take months to fully take hold, particularly if the public hesitates to return to normal without a vaccine or proven treatment.

Legal experts say Trump is likely on solid legal ground with the order, noting the Supreme Court granted the president broad authority on immigration after upholding a version of his travel ban in 2018.