After five minutes of trading, the Dow Jones industrial average rose 0.1 percent, the broad S&P 500 index rose 0.4 percent and the tech-heavy Nasdaq composite index rose 0.8 percent.
This follows Tuesday's fall as a result of US and Israeli actions against Iran.
But on Wednesday, things changed after reports in the New York Times claimed that Iran had contacted the United States via secret intelligence channels.
The US also promises military escort for tankers passing through the Strait of Hormuz.
The previously soaring oil price is turning down for the same reason the stock markets are rising. A barrel of North Sea oil costs $81.09, compared with $83.50 this morning.
The price of gas on the European market is also falling, but remains at relatively high levels.
