Parnell asked his attorney general and labor commissioner for recommendations after, his office says, he learned there would be a mandatory payroll contribution increase next year. Parnell said it would be "ludicrous" to require Alaskans pay more for unemployment insurance when the trust fund is solvent.
He wants to work with the Legislature, with any changes ensuring the future viability of the fund.
Parnell's office says the fund ended the third quarter with $234 million.
A formula in state law determines the unemployment insurance tax rate for employers. An additional $68 million will be collected next year, though Parnell's office says the fund would stay solvent without it.
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