In early trade on Monday, the S&P 500 was up about 7 points to 2,124.
Other major indexes also opened higher.
Near 10:00 a.m. ET, the Dow was up 64 points and the Nasdaq was up 20 points to 5,116, also an all-time high.
The Nasdaq crossed its closing high on Friday.
In economic data out Monday, the latest flash reading on service sector activity from Markit Economics came in at 57.8, down from 59.2 in March and missing the consensus of 58.2.
Apple shares climbed by as much as 2% ahead of its earnings report after the closing bell, which is expected to show another monster performance.