The broad S&P 500 and Nasdaq's technology-heavy composite indexes closed just below and just above zero, respectively, while the Dow Jones industrial average ended down 0.3 percent.
The downward pressure eased somewhat after Reuters published source information that American and Iranian negotiators on site in New York are reviewing a possible deal that would reopen the Strait of Hormuz.
Investors are also keeping an eye on longer-term US interest rates, which have continued to rise. The yield on the US 30-year Treasury bond reached its highest level since 2004 during the trading day.
Oil prices also continued to rise on Thursday, although the rise slowed somewhat later in the evening. A barrel of North Sea oil (Brent) now costs around $107.50.
