Federer and Williams added another major title to their respective collection earlier this month at Wimbledon, which is hosting the Olympic tennis tournament.
Federer, who along with Stanislas Wawrinka won an Olympic doubles gold medal for Switzerland four years ago, had to work harder than expected in his first-round match before getting past Alejandro Falla of Colombia 6-3, 5-7, 6-3.
Williams, who represents the best gold medal tennis hope for the United States, breezed past former No. 1 Jelena Jankovic of Serbia 6-3, 6-1.
The biggest threat to Federer in his quarter of the draw could come from American John Isner, who opened his Olympic bid with a 7-6, 6-4 decision over Oliver Rochus. If they both can get that far, Federer and Isner would meet in the quarterfinals.
Other opening-round winners in the men's draw included Denis Istomin of Uzbekistan, Philipp Petzschner of Germany, Janko Tipsarevic of Serbia and Tomas Berdych of the Czech Republic.
The win by Williams set up a second-round meeting with Urszula Radwanska of Poland, who defeated Mona Barthel of Germany 6-4, 6-3. Daniela Hantuchova of Slovakia rallied to down Li Na of China 2-6, 6-3, 6-3 and Ana Ivanovic of Serbia ousted American Christina McHale 6-4, 7-5.