Kasatkina, a former junior champion at Roland Garros, won the first set on a tie-break on Sunday evening but, in fading light, the players were taken off court at 3-3 in the second.
The other quarterfinal in the bottom half of the draw will match American Madison Keys, the No. 13 seed, against Yulia Putintseva, who now represents Kazakhstan after representing Russian Federation earlier in her career.
Having disposed of one reigning Grand Slam champion, Kasatkina will next face another in US Open victor Sloane Stephens.
Korea's Kim to Russian Federation
Mr Kim is always seen flanked by its generals on one side and civilians on the other when he attends major ceremonial events. In February 2016, he was briefly demoted to deputy chief and three stars from four for an unspecified reason.
Asus ROG Hero II gets your MOBA game on
If you're perhaps more of an Overwatch or Counter-Strike player, you may want to instead check out the ROG Strix Scar II instead. ROG Ryujin series also features Aura RGB lighting, along with reinforced sleeved tubing for better durability.
Suspect in Tenn. deputy's murder in custody, manhunt over
The man accused of a killing a Dickson County sheriff's deputy is in custody, according to the Tennessee Bureau of Investigation. A new trooper, Kevin Burch, was on patrol in Hickman County Friday morning when he saw a person near a woodline, according to Lt.
The crowd, who had been booing and doing the "Thunderclap" to try and make their feelings known, roared in approvement but they were set to be disappointed as just four games later the players once again went to the umpire and this time came off.
Earlier on Monday, top-seeded Simona Halep advanced to the French Open quarterfinals for the third time by beating Elise Mertens 6-2, 6-1.
"It was not that easy, she is a tough opponent", said Halep, who is chasing her maiden Grand Slam title.