At the close, the broad S&P 500 index and the technology-heavy Nasdaq's composite index had both risen 0.6 percent, while the Dow Jones industrial index had increased 0.3 percent.
Investors' caution is linked to the second round of trade negotiations in London between the US and China, where no more tangible results have yet been achieved than statements that "it's going well".
During Monday's equally fruitless search for news from London, the S&P 500 and Nasdaq's composite index rose slightly, while the Dow Jones industrial index closed unchanged.
On Tuesday, electric car company Tesla defied a warning from major bank Wells Fargo that the already battered stock may be subject to further pressure in a troubled and declining electric car market. Tesla climbed 5.7 percent.
On Tuesday, semiconductor giant Qualcomm, a leading manufacturer of processors for smartphones, presented a new processor that will be used in glasses with AI functions – both VR models and others. The stock rose 2.4 percent.
Another technology company that performed well was Alphabet (Google), up 1.4 percent.
Later in the week, important economic news will be released in the form of US consumer and producer price indexes, as well as a survey of consumer confidence in the US.
