European stocks turned lower Monday, as gains for mining stocks couldn't offset concerns about persistent strength in the euro as investors finished up trading for July. The Stoxx Europe 600 SXXP, -0.13% slipped 0.1% to close at 377.85, languishing at its lowest since April, according to FactSet data. Consumer-related, industrial and tech shares fell, but utility and health care stocks were among the advancers.

Equities continued to rise Tuesday, with Asian stocks starting August widely higher during what has been a strong earnings season so far. But there has been caution that further declines in the U.S. dollar, near its lowest levels in a year, could crimp results. A weaker dollar could make Asian exports less competitive over time.

The Dow industrials finished at an all-time high on Monday, but the broader market's gains were hobbled by losses in the technology sector. The Dow Jones Industrial Average DJIA, +0.28% gained 60.81 points, or 0.3%, to close at 21,891.12, pulling back from its best levels after hitting an intraday record earlier in the session at 21,929.80.