"In regards to the news that came out about us today… Any claims regarding us divorcing are untrue. However, yes, we have had a rough year," they wrote in his-and-hers posts shared on Instagram.
"The most challenging one of our marriage. But we both love and respect each other tremendously."
Earlier in the day, a source told People magazine, "Kyle and Mauricio have been separated for a while now but are still living under the same roof. They remain amicable as they figure out what’s next for them and their family."
Fox News Digital has reached out to Richards and Umansky for comment.
"There has been no wrongdoing on anyone's part," they continued. "Although we are in the public eye, we ask to be able to work through our issues privately. While it may be entertaining to speculate, please do not create false stories to fit a further salacious narrative."
Both turned comments off on their posts and signed off with gratitude, saying, "Thank you for the love and support."
The "Real Housewives of Beverly Hills" star has been married to The Agency real estate tycoon since 1996.
Richards and Umansky have three daughters together: Alexia, 27, Sophia, 23 and Portia, 15.
Richards also has daughter Farrah Brittany, 34, from her first marriage with Guraish Aldjufrie.
Richards, whose sisters include socialite Kathy Hilton and Kim Richards, is the last remaining original "RHOBH" cast member.
The "Halloween" franchise star joined the show at its inception in 2010, and viewers have watched her build new homes, new businesses and a new life as a successful producer and actress.
Richards' career in Hollywood began at an early age, when she worked as a child actress on "Little House on the Prairie," "The Car" and "The Watcher in the Woods." She also starred in the '80s sitcom, "Down to Earth," and appeared in more than a dozen episodes of the TV medical drama, "ER."
As Richards rebranded as a "Housewife" on Bravo, she also launched two self-named clothing collections and opened multiple boutique storefronts.
Viewers also caught a glimpse of Richards attempting to mend familial tensions with her older sisters, Kathy Hilton and Kim Richards.
Kathy's daughter, Paris Hilton, announced she welcomed a son via surrogate with her husband, Carter Reum, earlier this year.
Umansky has since built a global real estate business, The Agency, and boasts millions of sales annually.