Kalanick's decision "was a surprise to everyone", a second Uber spokesman said.
Dan Primack, business editor of the Axios news service, reported that there was increasing pressure for Kalanick to resign, particularly Bill Gurley of venture capitalist firm Benchmark. I will continue to serve on the board, and will be available in any and all ways to help Uber become everything we've dreamed it would be.
The investors included one of Uber's biggest shareholders, the venture capital firm Benchmark, which has one of its partners, Bill Gurley, on Uber's board.
As well as Mr Kalanick's immediate resignation, they demanded the board appoints more "truly independent directors" and that Uber hires an experienced finance chief.
"By stepping away, he's taking the time to heal from his personal tragedy while giving the company room to fully embrace this new chapter in Uber's history".
On Tuesday, Uber embarked on a 180-day programme to change its image by allowing riders to give drivers tips through the Uber app, something the company had resisted under Mr Kalanick. The blog post went viral and prompted Kalanick to launch an investigation into the culture of the organisation.
Holder said that Uber should "review and reallocate the responsibilities of Travis Kalanick" and search for a chief operating officer who would work closely with the new CEO to improve Uber's corporate culture. "He created a company that deceived local regulators, neglected the well-being of employees, wound-up drivers, troubled investors, obtained a rape victim's medical records and allegedly stole trade secrets from a rival".
The changes come as Uber works to fix the damage to its reputation following an investigation into allegations of sexual harassment, bullying and other employee concerns.
Despite recent turmoil, Uber's business is growing.