By Caitlin Ostroff and Dawn Lim

U.S. stocks ticked up modestly Tuesday as investors held out cautious hope for progress in Washington on an aid package to support an economy roiled by a pandemic.

The Dow Jones Industrial Average was up 0.62% as of the 4 p.m. close of trading in New York. The S&P 500 rose 0.36%. The technology-heavy Nasdaq Composite rose 0.35%.

Investors are monitoring negotiations among Democratic leaders and White House officials on a new coronavirus aid package. The two sides remain at odds over whether to cut a $600-a-week federal jobless supplement or provide aid to financially strapped states and localities.

"There's a bit of a pause if you will, as investors are waiting for confirmation on what the shape of the stimulus will be," said Lori Heinel, State Street Global Advisors's deputy global chief investment officer. "Clearly the market is looking for another sugar rush."

Ms. Heinel said the asset management firm is underweight stocks -- in other words, slightly below typically targeted to equities -- across its funds.

Many investors are on the sidelines of the stock market as they parse through the toll of Covid-19, which left millions unemployed and upended the economy. They are monitoring if a recent decline in new cases will hold up and how aggressively states will be able to stem the spread of the virus.

"One day's data doesn't mean anything, but I'm looking at whether that's the beginning of a trend," said Fahad Kamal, chief market strategist at Société Générale's private banking and wealth management division Kleinwort Hambros.

Although the pandemic has crimped profits for many businesses, more than three-quarters of S&P 500 companies have reported earnings, with the majority beating analyst expectations, according to UBS. This has led estimates for the third quarter to rise by 2.5% since the end of June.

Robust earnings from tech companies have lifted U.S. stock markets higher in recent weeks. The advances by big tech stocks is acknowledgment by investors that certain companies have become major beneficiaries as people rely more on software, cloud computing and social media to stay connected and to work from home. The technology industry made up at least 50% of that index for the first time since 2012, according to FactSet data as of Monday's close.

But the tech-heavy index showed muted gains Tuesday, and lagged behind the Russell 2000 index's 0.62% rise. This suggested that investors have questions about whether some tech names could be overpriced.

Facebook Inc. and Alphabet Inc. were both down more than 0.7%. Microsoft declined 1.7% amid uncertainty over whether it will be able to close a deal for U.S. operations of the hit video-sharing app TikTok. The deal would bring a Chinese technology crown jewel under U.S. ownership, but faces significant scrutiny in Washington.

Bond yields ticked lower. The yield on the 10-year Treasury declined to 0.520% from 0.562% Monday.

"There's more truth in the bond market, and if you look at the yields they're still at record lows. There's still a very palpable sense of fear among investors that there could be tail risks that materialize," Mr. Kamal said.

Front-month Comex Gold for August delivery, which gained $35.20 per troy ounce, or 1.79% to $2001.20. Front-month gold is on pace for its 8th record close in 9 trading days.

Richard Bernstein, chief investment officer of Richard Bernstein Advisors, said that gold's march is one indication that investors are uncertain about whether stimulus measures by Federal Reserve and U.S. government will translate to a broader recovery.

"The market does view it as a good cushion," he said, "But it's very uncertain over how it works it way into the economy.

Shares in Take-Two Interactive Software Inc., the company behind Grand Theft Auto and other gaming franchises, rose 4.7% after it raised financial projections for the year on higher demand for videogames during the pandemic. Shares in game maker Activision Blizzard rose 1.3%.

Shares in spirits maker Diageo, which owns Johnnie Walker whiskey and Smirnoff vodka among other brands, fell 5.55% after it reported that operating profit fell as the coronavirus pandemic drove down sales in the second half of the year. North American sales were strong as consumers shifted alcohol buying from bars to grocery stores, but the growth didn't make up for shortfalls in other markets.

In Europe, shares in BP climbed 6.48% after the British oil-and-gas producer slashed its quarterly dividend for the first time in a decade and launched a new strategy to pivot away from oil and gas. Discount airline easyJet rose 8.75% on a better-than-expected outlook.

In the Asia-Pacific region, Hong Kong's Hang Seng climbed 2%, leading gains in the region. Japan's Nikkei 225 gained 1.7%.

Write to Caitlin Ostroff at caitlin.ostroff@wsj.com and Dawn Lim at dawn.lim@wsj.com