TRENTON — The government shutdown may be over but the battle between Gov. Chris Christie and Assembly Speaker Vincent Prieto continues over the question of whether furloughed government employees will be paid for the Monday of the Fourth of July weekend.

In a letter to the governor on Friday, Prieto said government employees were being told they should file an unemployment claim for their involuntary day off on July 3. However, Prieto said that because of the formula for unemployment, "a very limited number of employees would qualify for unemployment benefits during the shutdown."

"This is neither a fair nor practical way to compensate state government workers who were not responsible for the shutdown and were, as always, more than willing to work that day," Prieto said.

Saying that the money to pay state employees was in the budget Christie signed to end the shutdown, Prieto said the governor could order the employees to receive their pay for that day.

"Doing so would be the quickest and most responsible way to resolve this question," he said.

In his response to Prieto's letter, Christie called the request "perplexing," saying that was not within his powers and said the Assembly should have followed the precedent set during the 2006 shutdown.

"You could have passed an appropriation bill in a timely manner, or you could have included an appropriation for this purpose in the bill you belatedly sent to my desk, like the Legislature did in 2006," Christie said. "Instead, you ignored the issue altogether in your budget bill and then sent me a letter that erroneously asked me to do something that is unlawful."

Christie said in his letter to Prieto that the Senate is currently considering an appropriations bill to pay the furloughed workers for July 3 and said the Assembly joining that effort "would be the most responsible way to resolve this issue."

"Your request to me to exert gubernatorial authority which I do not have is unlawful," Christie said. "As such, your request is denied, as it should be."

On Tuesday night, Prieto issued a statement calling Christie's claim that he could not use executive power on the issue "ridiculous."

The speaker also took aim at the governor, who has spent the past two days co-hosting the afternoon show on a New York radio station.

"At least he stepped away from his audition to spend a few minutes actually doing his job."

Prieto said he would "confer with members and the unions representing state workers on the best next step, including whether that should be legislation."

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