WASHINGTON—The first tax-filing season under the new tax law got off to a slower start than last year and filers so far are seeing smaller average refunds, according to early Internal Revenue Service data released Friday.

With about 10% of households filing their returns, the percentage of households getting tax refunds is similar to last year, but average refund size is down 8%, to $1,865. The number of returns filed so far—16 million—is down 12% from the similar point a year ago.

The first batch of weekly data from the IRS offers a very preliminary, unrepresentative look at what’s happening to taxpayers using the new tax system, which increased the standard deduction, lowered rates, and curbed some deductions. Typically, early filers are those who expect significant refunds, while those who owe money file closer to the mid-April deadline.

The picture will become clearer later this month, as tens of millions more returns are processed. The IRS is required to withhold certain refunds containing the earned-income tax credit and child tax credit until Feb. 15. The IRS, which had been partially shut down in the run-up to filing season, says it is running smoothly so far.

About two-thirds of households are getting tax cuts for 2018 under the law, and just 6% are paying more, according to the Tax Policy Center. But the size of those tax cuts may not be reflected in refunds, which are just the end-of-year reconciliation of what a taxpayer owes and what was withheld or paid during the year.

An expanded version of this report appears on WSJ.com

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