The broad S&P index increased by 2.5 percent, while the Dow Jones industrial index and the technology-heavy Nasdaq composite index both rose by 2.7 percent.
Despite the increases, investors are still uncertain about the outcome of the tariff negotiations between President Donald Trump's administration and several countries.
This was evident when reports emerged that US Finance Minister Scott Bessent had said at a meeting for investors that the trade war with China is unsustainable and that he expects the situation to de-escalate. The stock exchanges initially rose sharply after the reports were published, only to fall back slightly again.
The index-heavy technology companies known as "The magnificent seven" had a strong Tuesday.
iPhone manufacturer Apple rose by 3.4 percent, while e-commerce giant Amazon closed 3.5 percent up.
Google owner Alphabet, software giant Microsoft, semiconductor manufacturer Nvidia, and Meta (Facebook) all rose between 2 and 3.2 percent.
Electric car manufacturer Tesla, which is due to report its quarterly figures after the market closes, rose by 4.6 percent. The Tesla share has had a tough year and has fallen by around 40 percent since the turn of the year.
Streaming service Netflix closed 5.3 percent up.
Industrial conglomerate 3M impressed the market with its quarterly report, according to news agency AP. The share rose by 8.1 percent.
