U.S. stocks are swinging between small gains and losses at the start of the new trading week, after the S&P 500 finished last week at a new all-time high.

The Nasdaq index was recently down 0.1%, with the Dow losing a around 0.1% and the S&P 500 fractionally higher. Indexes in Asia finished mostly higher. A gauge of European stocks edged up.

Oil prices are rising, with Brent crude futures trading around $85 a barrel, as investors await major updates from the war with Iran. Over the weekend, Tehran laid out a list of demands for opening the Strait of Hormuz, including the U.S. withdrawing its forces, ending all sanctions and paying war reparations.

Focus remains on U.S. economic data and corporate results as second-quarter earnings season enters its final innings. It has been a blockbuster by several measures, with the S&P 500 headed for a seventh consecutive quarter of double-digit earnings growth.

Meanwhile, the big event this week will be Wednesday's inflation report for July. Economists expect it will show consumer prices up 3.4% from a year earlier, a slight improvement from the 3.5% inflation rate in June.