The French capital is heavily favoured to stage 2024, with the California metropolis having hinted that it was prepared to wait four more years.
The two cities were the remaining candidates for the 2024 Olympics, a contest that IOC boss Thomas Bach said created "a golden opportunity".
The Olympic movement has had increasing trouble attracting prospective hosts given the soaring costs and taxpayer support needed to put on the Games.
Bach lobbied for a double hosting plan, which won unanimous approval from IOC members at a meeting Tuesday in Lausanne, Switzerland.
With the deal in place, the IOC now has a two-month window to negotiate with Paris and Los Angeles over which city will go first.
Bach said he wants a "tripartite agreement" before the IOC's main annual meeting in Peru's capital Lima on September 13, when a vote on the 2024 host had been scheduled.
- Paris 'ready', LA to wait? -
Delegations from the two cities -- led by French President Emmanuel Macron and Los Angeles Mayor Eric Garcetti -- were in Lausanne to make fresh pitches to IOC voters.
Paris has maintained a tougher line on the 2028 question, insisting it was focused narrowly on 2024, the centenary anniversary of the city's last Games.
"I am here to convey a message to say our people are ready to host these Games," Macron told reporters.
"After three failed bids we don't want to lose a fourth one," he said.
Paris mounted losing bids for the 1992, 2008 and 2012 Games.
The Los Angeles team did little to quell speculation it was open to 2028.
"LA is ready to throw these Olympics in two months if we are asked, or two decades if it came to that because we have everything ready," Garcetti said, while noting the city was still "competing for 2024."
Bid chairman Casey Wasserman reminded that Los Angeles had not given the IOC "ultimatums" over the 2024 question.
The city last hosted the Games in 1984.
"Working hard to get the Olympics for the United States (L.A.). Stay tuned!" President Donald Trump said in a tweet, without making reference to a particular year.
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