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Tillerson spoke after reports that Vice President Mike Pence and other top officials intervened to persuade him not to resign during the summer as tensions rose with President Donald Trump.
"I have never considered leaving this post," said Tillerson. "I am here for as long as the President feels I can be useful to achieving his objectives."
Tillerson's comments come days after Health and Human Services Secretary Tom Price resigned under pressure from Trump following an uproar over Price's use of costly private charter planes for government business.
"The markets are going to breathe a sigh of relief that Tillerson is staying in office," said John Brady, senior vice president at futures brokerage R.J. O'Brien & Associates in Chicago.
"The markets are going to grind a little bit higher."
A drop in technology stocks had pulled down the S&P and the Nasdaq in early trading. The S&P information technology index, up about 26 percent this year, was on pace to post its first losses in seven sessions.
Meanwhile, data pointed to further strength in the economy.
The pace of growth in the U.S. economy's service sector accelerated in September to fastest in 12 years, led by stronger new orders and employment, according to an industry report released on Wednesday.
Also, the ADP National Employment Report indicated that private sector added a better-than-expected 135,000 jobs in September, even as Hurricane Harvey and Irma "significantly impacted smaller retailers."
The rest of the week is also loaded with economic data, culminating in Friday's nonfarm payrolls report for September.
The Nasdaq Composite was up 0.49 points, or 0.01 percent, at 6,532.21.
Six of the 11 major S&P indexes were higher, led by the healthcare, which got the biggest boost from Mylan.
Mylan surged 16.7 percent after the U.S. FDA approved the company's copycat version of Teva's blockbuster multiple sclerosis drug. Teva Pharmaceutical slumped 14 percent.
Advancing issues outnumbered decliners on the NYSE by 1,391 to 1,291. On the Nasdaq, 1,550 issues rose and 1,158 fell.
(Only the headline and picture of this report may have been reworked by the Business Standard staff; the rest of the content is auto-generated from a syndicated feed.)