Splitting up often means selling the house. But Shanghai couples dashed to split up on Monday so they could buy.

Spouses were scrambling to cut ties, at least on paper, amid rumors that the city might soon shut a loophole that families often use to buy more property: divorce. The surge is a response to concerns about rising property prices and government efforts to slow the increase.

Under current rules, a family buying a second home is required to put a down payment of up to 70% while a first-time buyer needs to put up only 30%. Widespread rumors—denied late Monday by housing authorities—say the penalty would be extended to those recently divorced for one year.

Dozens of couples packed into Shanghai's Xuhui District Divorce Registration Office to register divorces on Monday eager to break up. One woman, who gave her surname as Gu but declined to give her full name, said she was there to help her parents divorce after 35 years of marriage. The idea is to buy an apartment for the older couple that has an elevator, said Ms. Gu, and the divorce can help the "buyer" save on the down payment.

"We don't have much money, so there's no other way. The property price is so high that it's unbearable for us," Ms. Gu said. The divorce, she said, wouldn't destroy her family, because her parents have a stable relationship.

A paper divorce has been a way to circumvent the current restrictions, allowing one of the recently divorced partners to qualify for the lower downpayment. Ms. Gu said she had been considering a paper divorce for her parents since April and accelerated the process after hearing the rumor.

By afternoon at the Xuhui divorce office, just one of the Shanghai district offices inundated with sudden demand for divorces on Monday, a sign had gone up asking applicants to return another day. The office, on the third floor of a government office near Shanghai's South Station, said in the notice that the rush of applicants exceeded the center's capacity. It asked registrants to return later "to ensure service quality and guarantee the normal of order of marriage registration window"—which is adjacent to the divorce office.

Many wanted immediate service. Photos circulating online showed a line forming on the street outside a Huangpu District registration office early Monday morning; others showed the Pudong District office crowded with people.

Shanghai authorities have already rolled out measures to cool the local real-estate market this year. The government banned peer-to-peer lending as a funding tool for down payments and raised the down-payment rate for certain second homes. The restrictions seemed to have some impact, as home-price gains softened over the summer, though they still surged 27.3% in July from a year earlier, according to the National Bureau of Statistics.

Late last week and over the weekend, rumors circulated anew that Shanghai would again make it harder to buy and sell homes, sparking a rush to close housing deals. Last Friday, Shanghai's real-estate transaction center said its website crashed for about an hour, apparently due to a connection failure after web traffic surged.

Daily transactions for new homes on Monday topped 1,000 for the third day in a row. Transactions for new homes averaged 600-700 per day in July.

At the Xuhui District divorce office on Monday, a 32-year-old man and his pregnant wife were among those waiting to end their marriage of five-plus years. The couple declined to give their names but said they want to upgrade their two-bedroom apartment by purchasing a bigger one with three bedrooms to make way for the baby—their second—due in October. Divorce, they calculated, is the only way they can afford to fulfill the plan.

As a couple, they face an initial 70% payment for the new 4.3 million yuan (about $643,900) apartment. Divorced, one of them could do a deal with only a 30% initial payment. When a staff member at the registration desk told the wife that she might run into additional barriers for getting divorced because of her big belly, she cried. "We don't have any other way out," she said.

Late Monday, Shanghai's commission of housing and urban-rural development issued a denial via its official Weibo microblog that authorities will shortly impose new limits on home purchases.

-- Dominique Fong, Junya Qian and Yifan Xie