US stocks posted modest gains on Tuesday, driven by NVIDIA's advance ahead of its Wednesday earnings release, while traders assessed Trump's decision to dismiss Federal Reserve Governor Cook.

The S&P 500 index rose 0.4%, with NVIDIA leading large-cap stock gains as the company prepares to announce its results.

UnitedHealth Group declined amid reports that the ongoing criminal investigation into the company allegedly extends beyond potential Medicare fraud.

Eli Lilly was the top performer in the S&P 500, surging nearly 6% after its experimental weight-loss drug helped patients lose 9.6% of their body weight in clinical trials, bringing the company closer to potential approval.

Keurig Dr Pepper Inc. was the biggest drag on the S&P 500, falling 6.9% on Tuesday following Monday's sharp decline, after the company announced plans to acquire Dutch tea and coffee giant JDE Peet's for $18 billion.

Regarding the dismissal of Fed Chair Cook, Trump indicated he is prepared for a legal battle. The Federal Reserve commented on the matter for the first time this week, stating it would comply with any court ruling.

"Trump's push to fire Cook has heightened concerns about Fed independence," said Ian Lyngen of BMO Capital Markets. "While Treasury yields have largely remained within recent ranges, many common hedging strategies against erosion of Fed independence have performed well since news of Cook's dismissal emerged."

"An independent Fed remains the dominant framework," said Dennis DeBusschere of 22V Research. "There's no reason to oppose this framework yet, but hedging is important."

"This issue may end up being resolved in court," said Brad Bechtel of Jefferies. "If this dismissal actually goes through, Trump would obviously have another seat to fill, which from a political standpoint should make the board more favorable to him."

"Consumers don't seem scared but may be showing restraint," said Bret Kenwell of eToro. "Corporate conference calls suggest consumers appear resilient, and retail sales data confirms similar reassuring signs."

At the close, the S&P 500 index gained 0.41% to 6,465.94 points;

The Dow Jones Industrial Average rose 0.3% to 45,418.07 points;

The Nasdaq Composite advanced 0.44% to 21,544.27 points.