By Eric Sylvers and Ben Dummett

John Elkann, scion of the Agnelli family that controls Fiat Chrysler Automobiles NV, sealed two deals that would have helped him diversify his family's holding company. Now, one has come undone, and the pressure is on him to save the other.

Last week, his $9 billion planned sale of insurance company PartnerRe Ltd. fell apart when the buyer walked away before closing. And Mr. Elkann's planned merger of Fiat Chrysler and Peugeot maker PSA Group is under sudden strain.

Mr. Elkann, the 44-year-old chairman of both Fiat Chrysler and Agnelli family holding company Exor NV, played a leading role in negotiating both pacts, according to people familiar with the matter. That has lifted him into a high-profile role in a global drama playing out among deal makers trying to keep their big, unfinished transactions on track amid the coronavirus pandemic.

"Given the unchartered waters we are in, Elkann's deal savviness is being put to the test," said Tyler Tebbs, an analyst at Olivetree Financial, a research firm that focuses on merger-and-acquisition transactions.

Mr. Elkann declined to comment. In prepared comments about the Peugeot deal released Wednesday and coinciding with Exor's annual shareholder meeting, he said "all the workstreams for the 50:50 merger project...are proceeding on time and as envisaged. The strategic logic of this combination for the two companies and all their employees is stronger than ever."

Several big M&A pacts forged before the pandemic have recently come undone, including Xerox Holdings Corp.'s $30 billion bid for HP Inc. and Boeing Co.'s $4.2 billion deal to take control of the commercial aircraft business of Embraer SA.

Executives on both sides of the Fiat Chrysler-Peugeot deal say the merger makes more sense now than ever by combining the two auto makers' financial resources and geographic markets. The two sides say they expect the deal to close as planned before the end of the first quarter of next year.

A big component of the tie-up, though, is a series of cash payouts to shareholders at a time when cash preservation is core to many companies' pandemic-survival plans. The payouts initially included planned annual 2019 dividends of EUR1.1 billion ($1.2 billion) for each company. The two canceled those dividends this month.

The deal also calls for a further EUR5.5 billion payout to Fiat Chrysler shareholders, to help make up for an imbalance in the two companies' respective values in their so-called merger of equals. Exor owns 29% of Fiat Chrysler, entitling it to EUR1.6 billion of that. Following the deal's completion, Exor's stake in the combined company would be diluted to about 14%.

Some analysts and investors criticized the size of the planned payouts as too generous even before the economic fallout of the pandemic forced big companies to rush for cash.

That has the market increasingly worried Peugeot could push Fiat Chrysler to cut the dividend or restructure the payout to include some types of shares over cash, arguing such a move would leave the combined company in better health following the deal's completion.

However, it would also risk the deal's collapse by giving Fiat Chrysler a possible out since the terms are binding. At the very least, any attempt to renegotiate the deal by either side could prolong and further complicate an already detailed tie-up at a time when both car makers have stressed the deal's importance to their long-term success.

"It's set in stone, as contracts binding in their nature are," Mr. Elkann told analysts on a conference call on Wednesday, dismissing the idea that the deal terms could be reworked.

In March, Fiat Chrysler secured a EUR3.5 billion credit line with its banks to weather the storm. It is also discussing another EUR6.3 billion Italian government-backed facility. Fiat Chrysler said that at the end of March it had about EUR18 billion in cash and liquid assets.

Fresh off the Fiat Chrysler-Peugeot merger, Mr. Elkann agreed to sell Exor's reinsurance business, PartnerRe, to French insurance giant Covéa Coopérations for $9 billion. Exor said it hadn't been looking to sell the unit, but the Covéa offer was too good to pass up. Exor bought PartnerRe in 2016 for $6.9 billion.

As the pandemic deepened, Covéa approached Exor to renegotiate the deal, according to people familiar with the matter. It was looking to cut the upfront price by about EUR2 billion, according to these people. The new terms would have called for Covéa eventually restoring the original $9 billion price tag -- but only if the unit met certain benchmarks, these people said.

Mr. Elkann said no. Exor wouldn't be able to exert control over PartnerRe, making hitting those performance benchmarks uncertain, the people said. Mr. Elkann had another reason for balking: He wanted to send a signal that he wasn't willing to renegotiate other done deals, including the Fiat Chrysler-Peugeot merger, one of these people said.

"If you cede on one deal, people are going to think they can cut the price on you every time in the future," this person said. "And John is going to be doing deals for many years to come."

Wednesday on the call with analysts, Mr. Elkann said that Exor is happy to retain ownership of PartnerRe and that he thinks it is worth more now than before the epidemic.

Mr. Elkann, the great-great-grandson of Fiat founder Giovanni Agnelli, has been the Agnelli family's undisputed leader since 2004. But he had long let Sergio Marchionne, Fiat Chrysler's former chief executive who died unexpectedly in 2018, take the lead running the company. Mr. Marchionne also led the charge in both men's longtime pursuit of a partner for Fiat Chrysler. When Fiat Chrysler broached a combination with General Motors Inc. in 2015, it was Mr. Marchionne who reached out to his rival.

With Mr. Marchionne's death, Mr. Elkann took a more direct role in the search. Early last year, preliminary talks with Peugeot went cold. He then turned to rival Renault SA. Those talks, too, unraveled after the French government and Renault partner Nissan Motors Co. failed to back the deal. Mr. Elkann reverted to Peugeot and the two struck a merger deal last year, first reported by The Wall Street Journal.

Mr. Elkann has enjoyed strong support over recent years from family members, according to people familiar with the matter. That stood in contrast with a history of public family squabbles since the death of Mr. Elkann's grandfather, Gianni. The playboy industrialist turned his own grandfather's company into a postwar giant, earning the nickname the "King of Italy." Exor's hefty dividends in recent years, made possible by the return to health of Fiat Chrysler and the strong results of other holdings, have helped Mr. Elkann win the family's backing, according to people familiar with the matter.

Mr. Elkann has led the family's fitful effort to diversify away from autos and into other areas including technology. In addition to the stake in Fiat Chrysler, Exor owns 23% of Ferrari NV, almost two-thirds of Italian soccer club Juventus and 27% of agricultural equipment maker CNH Industrial NV.

He had been expected to direct the most of proceeds from the two deals into new investments. In March, Exor spent EUR200 million for a 9% stake in startup Via Transportation, which is building ride-sharing technology for public transportation.

Write to Eric Sylvers at eric.sylvers@wsj.com and Ben Dummett at ben.dummett@wsj.com