U.S. chain store sales were mixed last week, as solid demand for back-to-school items were offset by cooler weather and the end of sales tax holidays, two reports showed on Tuesday.

Sales at major retailers were up 3.3 percent on a year-over-year basis for the week ended August 19, following a 3.2 percent gain the previous week, said Redbook Research, an independent company.

Sales at U.S. retailers have risen 0.3 percent so far in August when compared with the same period in July.

Back-to-school sales were active over the last week as school years neared beginning, Redbook said in a statement.

Cooler weather spurred buying of back-to-school and fall clothing, but may have suppressed demand for seasonal summer items like air conditioners as well as outdoor and sporting equipment, the research firm said.

Meanwhile, the International Council of Shopping Centers and UBS said sales dipped 0.2 percent last week, compared with an unchanged level in the previous week.

Compared with the same week in 2005, sales rose 2.7 percent, a tad higher than the 2.6 percent year-ago rise the preceding week, ICSC and UBS said.

With the end of sales tax holidays in the bulk of the states and the lack of sales urgency, customers decided to take a break this past week, Michael Niemira, ICSC's chief economist said in a statement