Aug 30 (Reuters) - The S&P 500 and Nasdaq hit all-time highs on Monday as dovish remarks from the Federal Reserve last week bolstered optimism in an economic rebound and eased fears of a sudden tapering in monetary stimulus. The Dow Jones Industrial Average rose 16 points, or 0.05%, at the open to 35,471.8. The S&P 500 rose 4.4 points, or 0.10%, at the open to 4,513.76, while the Nasdaq Composite rose 36.4 points, or 0.24%, to 15,165.94 at the opening bell. (Reporting by Sruthi Shankar in Bengaluru; Editing by Arun Koyyur) Our Standards: The Thomson Reuters Trust Principles.