US equity indexes fell during midday trading on Tuesday as Treasury yields rose amid growing uncertainty over the US-Iran conflict and faltering consumer confidence in September.

US President Donald Trump denied an Axios report that he had offered Tehran sanctions relief and to release Iran's frozen funds in return for concrete steps regarding the country's nuclear program.

Iran's Revolutionary Guard spokesperson Gen. Hossein Mohebbi read a letter addressed to the "American people" during a Tuesday news conference, mentioning that the only way for the conflict to end is for the US government to admit defeat and leave, according to the Associated Press.

The Nasdaq Composite fell 0.1% to 26,794.1. The Dow Jones Industrial Average fell 0.6% to 51,156.2, while the S&P 500 declined by 0.3% to 7,660.5. Health and financial sectors led the decliners.

The 10-year US Treasury yield climbed 3.2 basis points to 5.27% and the 30-year rate rose 4.1 basis points to 5.60%.

The US West Texas Intermediate crude oil contract fell 2.3% to $90.50 per barrel.

In economic news, The Conference Board's measure of consumer confidence fell to 81.9 in September from 88.6 in the month prior, compared with an expected rise to 89.0 in a Bloomberg-compiled survey.

"References to prices, the high cost of goods and services, and oil and gas prices in particular, rose to new heights, reflecting September's surge in fuel costs," said Dana Peterson, chief economist at The Conference Board.

US job openings in August declined to 7.079 million from 7.335 million openings in July, according to the Bureau of Labor Statistics, compared with 7.228 million openings expected in a Bloomberg-compiled survey. Hiring rose to 5.192 million in August from 5.146 million in July, while separations decreased in the month to 5.070 million from 5.128 million in July.

The Federal Housing Finance Agency said Tuesday that US single-family home prices in July rose 0.3% nationwide, after a flat reading in the previous month, and above the 0.1% gain expected in a Bloomberg-compiled survey.

In company news, AT&T (T) and Corning (GLW) agreed to a multi-year deal worth over $3 billion for Corning to supply fiber and cable to support AT&T's network expansion roadmap, the companies said Tuesday. AT&T shares were down 0.5%, while Corning shares were up 4%.