After holding talks with Hassan Wirajuda, Indonesia's foreign minister, on Wednesday, Clinton said the two countries intended to co-operate in areas ranging from security and counter-terrorism to climate change.
"Building a comprehensive partnership with Indonesia is a critical step on behalf of the United States' commitment to smart power to ... speak to a country that has demonstrated that Islam and modernity can not only co-exist but thrive together," she said.
On the second leg of a weeklong tour of Asia, Clinton said it was "no accident" that Indonesia had been picked as one of her four stops.
But the chief US diplomat got an icy reception with a few hundred protestors shouting slogans against her and throwing shoes at a caricature of her on Wednesday.
Clinton heads to South Korea later on Thursday before wrapping up her trip with a stop in China later in the week.
Her visit to Seoul comes as tensions mount on the Korean peninsula, with Pyongyang saying on Thursday that it was ready for war and repeatedly threatening in recent weeks to reduce the South to ashes.
Pyongyang is thought to be readying its longest-range missile for launch in what analysts say is a bid to grab the new US administration's attention and press South Korea's president, Lee Myung-bak, to soften his hardline stance against it.
Speaking in Tokyo on Tuesday as she began her first foreign trip since taking office, Clinton said that a North Korean missile launch would be "very unhelpful".