The tax-exempt market continued to outperform Treasuries Thursday morning as the muni selloff was much more muted than the Treasury selloff.

Traders in the municipal bond market said munis were steady to just a tad weaker. While munis yields generally follow Treasury yields higher, limited supply and fresh reinvestment money has kept the market mostly steady.

"There is a fair amount of trading going on in munis," a New York trader said. "But munis are holding in there and through 15 years they are holding in fairly well. You haven't had new issues over the past few weeks and there shouldn't be a lot of supply next week so with the reinvestment money munis should outperform."

On Wednesday, the Municipal Market Data scale finished slightly weaker, with yields rising one to two basis points across the curve. But after the MMD scale was adjusted for the January roll, yields were marked up between one and eight basis points.

Overall, the two-year MMD yield - now a 2015 maturity - rose five basis points to 0.36%. The 10-year MMD yield - now a 2023 maturity - finished six basis points higher at 1.78%. The 30-year MMD yield - now a 2043 maturity - closed three basis points higher at 2.86%.

Treasuries continued to weaken Thursday morning after a large selloff Wednesday. The benchmark 10-year yield rose two basis points to 1.86% while the 30-year yield increased three basis points to 3.07%. The two-year yield rose one basis point to 0.27%.

In economic news, initial jobless claims rose 10,000 to 372,000 for the week ending Dec. 29. Continuing claims were up 44,000 to 3.245 million for the week ending Dec. 22.

"We have to be careful not to read too much into year-end claims data because of volatility associated with shifting holidays and seasonality that is not necessarily adequately adjusted for by the usual statistical procedures," wrote economists at RDQ Economics. "The four-week average of claims has fallen sharply since the Sandy-related surge and the last two weeks' readings were the lowest since March 2008, while layoff announcements in 2012 were 13.6% below the pace reported in 2011. We believe the key to job creation is the pace at which companies are willing to hire new workers since it appears they are already retaining existing employees at a high rate."

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