Stocks climbed on Tuesday as investors hoped for a positive resolution on trade discussions between the U.S. and China.

The Dow Jones Industrial Average added 105.11 points, or 0.25%, and closed at 42,866.87. The S&P 500 rose 0.55% to end at 6,038.81, while the Nasdaq Composite gained 0.63% and settled at 19,714.99. It was the third positive session for both indexes.

Talks between U.S. and Chinese officials in London continued for the second day. U.S. Commerce Secretary Howard Lutnick said he hopes the discussions will end Tuesday night, adding that they could run into Wednesday if need be.

"I think the talks are going really, really well. We're very much spending time and effort and energy - everybody's got their head down working closely," Lutnick told reporters on Tuesday in London.

Traders are monitoring the discussions for signs of a deal that doesn't involve the countries enforcing lofty tariffs on one another. Both nations agreed last month to temporarily slash their duties, which was seen as a major breakthrough in trade negotiations after U.S. President Donald Trump unveiled his plan for broad and steep levies on imports.

Stocks have rallied so far in June as investors remain hopeful about ongoing global trade discussions and overall strength in the market. Gains have been powered by strong corporate earnings results and a revival in tech stocks, given the recent slew of artificial intelligence announcements.

"Technically, shares have been on a nice run eclipsing key levels to get back on track. Longer term, they started the week right above its downtrend line going back to its annual highs," said Jay Woods, chief global strategist of Freedom Capital Markets.

"The rally looks like many other technology names that are trying to get back to old highs. The good news is that given the change in trajectory, even weakness looks to have a soft landing spot and good entry point from a risk/reward perspective," Woods added.

To be sure, some investors are concerned that the current tariffs could drive inflation higher in the near future, potentially weighing on equities.

"While the picture is not completely clear, enforceable tariffs exist," said Mark Malek, chief investment officer of Siebert Financial. "The Fed is concerned that the real inflationary effects have not yet shown up yet. Based on the complex collection of tariffs in effect today, we would expect aggregates such as autos, apparel, and foods to show initial signs of tariff-driven inflation."