Sen. Jeff Sessions Jefferson (Jeff) Beauregard SessionsGOP set to release controversial Biden report Trump's policies on refugees are as simple as ABCs Ocasio-Cortez, Velázquez call for convention to decide Puerto Rico status MORE (R-Ala.) on Thursday said he could still back Donald Trump Donald John TrumpBiden leads Trump by 36 points nationally among Latinos: poll Trump dismisses climate change role in fires, says Newsom needs to manage forest better Jimmy Kimmel hits Trump for rallies while hosting Emmy Awards MORE's immigration plans amid controversy over the Republican presidential nominee's recent softening of his stance.

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"Oh yeah, I can be supportive of that," Sessions told "Fox and Friends" when asked if he could get on board with Trump's proposal on how to deal with longtime undocumented immigrants.

During a town hall earlier this week, Trump raised the idea that undocumented immigrants who have been in the country for a long time could pay back taxes and "we [could] work with them." Trump clarified Thursday that there would be no amnesty granted.

"I think what he's saying is let's prove the weakness in so many of the plans that have been offered over the years is that they’ve given amnesty first and promised enforcement in the future," Sessions said.

"He’s saying: 'Let’s fix this problem. Let’s fix it, and then we’ll wrestle with people who have been here a long time.' I think that's the right approach. But you have to be careful because you’ve got have the rule of law," he said.

Earlier this week, Sessions said that it appeared Trump was "wrestling" with the issue of what to do about people who have been in the country for a long time and haven't had any legal issues.