"A strong recovery that creates jobs, income and spending is the most important contribution the United States can make to the global recovery," said the letter, as Obama arrived in Seoul for the two-day summit starting Thursday.
"The dollar's strength ultimately rests on the fundamental strength of the US economy," he wrote, after widespread criticism from other G20 powers that his administration is trying to devalue its way back to prosperity.
President Jacob Zuma arrived in Seoul on Wednesday to attend the fifth G20 summit, the department of international relations and co-operation said.
"South Africa is part of the G20 as is systematically important for [a] country with national economic interests to promote," said spokesman Saul Molobi.
It will focus on developing a "framework for strong, sustainable and balanced growth, strengthening the international financial regulatory system, [creating] global financial safety nets and modernising the international financial institutions".