Tufte, needing only to finish among the first three in his heat to make it to the quarterfinals, wound up second behind 2008 bronze medalist Mahe Drysdale of New Zealand.
The United States' eights crew, meanwhile, won its qualifying heat in a bid to challenge Germany in the highlight rowing competition at the Olympics.
Germany, a traditional rowing power but without a medal in the men's eights during the last three Olympics, turned in a time of 5:25.52 over the 2,000-meter course. The United States crew was timed in 5:30.72.
The gold medal in the eights will be awarded Thursday.
All six finalists from the 2008 Games are entered again in the men's single sculls with Tufte seeking his third consecutive gold medal at the age of 36.
Ondrej Synek of the Czech Republic, who finished second to Tufte in Beijing four years ago, won his qualifying heat Saturday with a time 6:53.23. Tufte's time was 7:00.90 and Drysdale was clocked in 6:49.69.
In the women's pairs qualifying, the United States duo of Sara Hendershot and Sarah Zelenka made it to the finals by finishing second to the British team of Helen Glover and Heather Stanning.
Having turned in the second-fastest qualifying time, Hendershot and Zelenka have a good chance to earn the first medal in the event for the United States since the 2000 Olympics in Sydney.
Notable deaths of 2014 [PHOTOS]