Major U.S. brokerage firms reported outages or slowly running customer websites on Tuesday during another day of volatile trading as the U.S. stock markets reversed a sharp downturn.

A Fidelity spokesman said late Tuesday morning that the firm, with $2.2 trillion under management, resolved intermittent technical issues on its website. A message on its website earlier in the morning said, "Our homepage is temporarily unavailable but don't worry, we're working quickly to fix this problem."

TD Ameritrade said in a message on its website: "Due to volatile market conditions we are currently experiencing slowness on our web platform." It advised people to try one of its mobile apps or a related company website.

On Twitter, people complained they were unable to access Merrill Edge, a brokerage website operated by Bank of America. A spokesman said in a statement, "Our systems remain operational. Some clients reported slowness logging into My Merrill and Merrill Edge due to unprecedented trading volume."

After falling a record-setting 1,175 points on Monday, the Dow Jones industrial average opened sharply down again on Tuesday before climbing back into positive territory during the first half-hour of trading in New York. As of 11:52 a.m. ET, the Dow was up 52 points.

On Monday, a few brokerages reported temporary issues or slowness on their customer websites, including T. Rowe Price and TD Ameritrade, that were resolved. Fidelity told CNBC its customers remained calm, and its website appeared to have no issues.

Fidelity had some temporary outages on its website in November that blocked customers from accessing their online accounts and offered free trades to compensate.