At the close, the broad S&P 500 index had climbed 1.2 percent, the tech-heavy Nasdaq composite index had risen 2.1 percent, while the Dow Jones industrial average gained 0.6 percent.
Google's parent company Alphabet rose by around 5 percent, making it one of the clear winners of the day.
The weekend's reports that the US and Iran had agreed to pause their attacks were followed on Monday by the announcement that the parties would meet in Qatar this week for continued talks, something that investors have apparently taken note of.
The price of oil edged up slightly on Monday. At 10 p.m., a barrel of North Sea oil cost around $73.
