Sen.-elect Mitt Romney (R., Utah) said Wednesday that he not only supports a wall on the U.S.-Mexico border, but also strengthening the E-Verify system to penalize employers who hire illegal immigrants.

Responding to outgoing Sen. Bob Corker's (R., Tenn.) charge that the government shutdown is a "made-up fight" ginned up by President Donald Trump, Romney said the shutdown is regrettable but a border wall is necessary. Romney said that his stance on strengthening border security has been consistent, adding that companies should be prevented from hiring illegal immigrants.

"I think the president is very sincere when he says he wants to secure the border, and how you get there is a real question. It's going to have to be worked out on a bipartisan basis," Romney said on CNN. "Clearly, we have to have a more secure border. And I think that really should focus on the E-Verify system, which basically penalizes employers if they hire people that are here illegally."

The federal government uses the E-Verify system to make sure that contractors hire employees who are legally allowed to work in the United States. Some advocates of stricter immigration laws are calling for Trump to expand the reach of E-Verify through an executive order, the Washington Examiner recently reported.

When CNN host Jake Tapper pressed Romney on how he would handle the government shutdown, the senator-elect said he would push for funding a border wall in addition to other security measures.

"I would vote for the border wall. I've made that part of my platform for many, many years. I think we should have a border wall on our southern border, whether it's a wall or a fence or technology, and perhaps in some cases the natural landscape prevents people from coming into the country easily," he said. "But that's necessary but insufficient. We have to do a lot more in terms of our E-Verify system, in terms of our visa-tracking systems and so forth."

Romney also said he supports letting states' needs determine how temporary work visas are apportioned.

"We need to make it easier in some respects for people to come here legally and work temporarily and then go home, particularly in the agriculture industry," he said. "In Utah, we rely on a lot of people coming in to harvest crops and so forth. We ought to let that be guided by what the states need as opposed to what the federal government imposes on them."

Romney took flak from Trump and other Republicans for writing an op-ed this week critical of the president's character and decisions. Elsewhere in the CNN interview, Romney said he does not want to run against Trump in 2020 but has not decided whether he will support him.