About 45 minutes into trade, the Dow Jones Industrial Average rose 56.51 (0.35 percent) to 16,414.06.
The broad-based S&P 500 added 4.26 (0.23 percent) at 1,837.58, while the tech-rich Nasdaq Composite Index increased 9.74 (0.23 percent) to 4,165.16.
First-time claims for US unemployment benefits fell to 338,000 from an adjusted 380,000 the previous week, the Labor Department said. Analysts had projected that 350,000 claims would be filed.
The decline in claims, the greatest in a weekly report since November 2012, came on the heels of a stream of largely-positive US economic data in recent days, including strong reports on third-quarter economic growth and November durable goods.
The Dow and S&P 500 closed at fresh records in the three sessions prior to Wednesday's Christmas holiday, when markets were closed.
Trading volume was light Thursday, as many international exchanges remained closed, analysts said.
Corporate news was also light, but a number of stocks recorded notable movements.
They include: 3D printer company 3D Systems (+5.3 percent), in-flight telecommunications company Gogo (+6.2 percent), tanker company DryShips (+7.2 percent) and retailer J.C. Penney (+2.2 percent).
Telecom company Sprint rose 3.1 percent following a report that its parent SoftBank is in talks to purchase US wireless company T-Mobile. T-Mobile rose 1.0 percent.
Bond prices slipped. The yield on the 10-year US Treasury rose to 2.99 percent from 2.98 percent, while the 30-year increased to 3.91 percent from 3.90 percent. Bond prices and yields move inversely.