By Alexander Osipovich and Corrie Driebusch

Nasdaq Inc. has edged past the New York Stock Exchange in initial public offerings this year as the coronavirus pandemic has curtailed activity and reined in celebrations of corporate debuts on the NYSE's historic trading floor.

Companies going public in 2020 raised $12.2 billion in IPOs at Nasdaq through Friday, compared with $10.9 billion at the NYSE, Dealogic data show. Nasdaq lagged behind the NYSE for much of the year but pulled ahead after hosting several large debuts last week, including that of Warner Music Group Corp., which raised more than $1.9 billion in the year's largest IPO to date.

IPO activity plummeted in March, when fallout from the coronavirus hammered stock prices and led a number of companies to postpone or scuttle plans to go public. But with the S&P 500 staging an extraordinary rebound in recent weeks, many have revived their IPO plans, leading the two rival exchanges to reinvigorate their fight for each new listing.

The NYSE could still pull ahead of Nasdaq this year by winning a few large IPOs, such as grocery giant Albertsons Cos., which said in a March regulatory filing that it had been approved to list on the NYSE. Other companies planning to debut in the coming weeks include used-car marketplace Vroom Inc., which is expected to list on Nasdaq.

On Monday, Royalty Pharma PLC launched its IPO roadshow to pitch shares to prospective investors. The pharmaceutical company aims to raise nearly $1.9 billion in its IPO at the midpoint of its target-price range and plans to list on Nasdaq, according to a regulatory filing.

NYSE executives say it is misleading to judge performance purely by capital raised in IPOs. By a broader measure of capital raised -- including follow-on offerings by listed companies and new listings of closed-end funds -- the NYSE is ahead of Nasdaq, they say.

"The NYSE is the world leader in capital raising, with more proceeds from IPOs and follow-on offerings than any global exchange," John Tuttle, the NYSE's vice chairman and chief commercial officer, said in an emailed statement. "Our leadership stems from our unwavering commitment to issuers and ability to provide the very best marketplace for their shares."

The NYSE and Nasdaq make money by collecting companies' listing fees, along with several other revenue streams. Nasdaq is cheaper for many companies: Both exchanges charge varying amounts based on companies' number of shares outstanding, but Nasdaq's fees are capped at $159,000 annually, while the NYSE's run up to $500,000.

Although that isn't a big difference for large companies, it could still work to Nasdaq's advantage this year. Since the turmoil caused by the pandemic, corporate boards have become increasingly concerned about how their cash is spent, according to bankers and board members.

Late last month, oil producer Apache Corp. said it would switch its primary listing exchange to Nasdaq from the NYSE, citing cost considerations. Like other energy companies, Apache has been battered by the slump in oil prices.

Nasdaq is planning a push to attract more companies to switch over from the NYSE, and it expects to have an advantage thanks to its lower costs, Nelson Griggs, Nasdaq executive vice president, said in an interview.

"When the pandemic hit, some companies were very challenged," he said. "Now companies are planning for next year, and obviously costs are a consideration."

Traditionally, the NYSE has been the home of blue-chip stocks and attracted more big listings than Nasdaq. During the past decade, Nasdaq beat the NYSE in capital raised in IPOs only twice, in 2012 and 2019, according to Dealogic.

But this year has been a tough one for the NYSE, which is owned by Atlanta-based Intercontinental Exchange Inc. The coronavirus forced the NYSE to shut its floor for two months, after two people at the exchange tested positive for Covid-19.

Although closing the floor had little impact on investors -- the NYSE's markets continued to function in all-electronic mode -- it disrupted the exchange's playbook for winning IPOs. Debuts at the Big Board typically involve parties and bell-ringing ceremonies at its building on the corner of Wall and Broad streets in Manhattan, a once-in-a-lifetime media and branding opportunity for many companies.

During the floor closure, companies did virtual bell-ringings at the NYSE, using a video link. That has begun to change since the floor reopened May 26 with strict new social-distancing rules. On Friday, Shift4 Payments Inc. Chief Executive Jared Isaacman became the first CEO of a company doing an NYSE IPO to ring the opening bell in person since the reopening.

Still, the company's debut was subdued compared with past IPO celebrations, with no party in the Big Board's ornate event spaces and only three people -- Mr. Isaacson, one of his investors and NYSE President Stacey Cunningham -- on the bell-ringing podium. Before the pandemic, a dozen or so company representatives would often crowd onto the podium for IPOs. Mr. Isaacson said there will be a more formal celebration, with Champagne, for employees in the future.

"The floor has been a superb marketing weapon for NYSE," said Patrick Healy, CEO of Issuer Network LLC, which advises companies on their choice of listing exchange. "Without that weapon, they're not quite the same."

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Write to Alexander Osipovich at alexander.osipovich@dowjones.com and Corrie Driebusch at corrie.driebusch@wsj.com