"So for a president, knowing he can go somewhere in the world where he is so loved as he is loved in Indonesia, he may just want to wait until he really needs that visit," said Clinton, triggering laughter.
"You can lavish on him all of the love that you're telling me you feel for him," the former first lady told Indonesian civil society members, including human rights activists, environmentalists and religious leaders.
"So I will speak with him soon and tell him that he is well-liked and well-regarded and that he should look for the opportunity to come as soon as his schedule permits," she added.
After landing in Jakarta on a flight from Tokyo, Clinton was greeted by senior officials and a choir of students from Obama's old Menteng One primary school in the city.
Clinton, wearing a red coat over a black blouse and trousers, nodded along with the smiling, singing children who raised Indonesian and American flags.
The personal connection with Indonesia has helped make Obama a huge figure in the world's most populous Muslim-majority country.
The son of a white American mother and a black Kenyan father, Obama was raised in Hawaii and moved to Indonesia when he was six after his mother remarried an Indonesian.
While the vast majority of the massive archipelago's 234 million people are moderate Muslims, Indonesia has seen its share of Islamist violence -- including the 2002 Bali nightclub bombings that killed more than 200 people.
A small fringe of radical extremists continues to call for "holy war" against the West and demands the implementation of hardline sharia law in the country.
Extremist groups have rejected Obama's attempts to reach out, saying Washington merely wants to use Indonesia to window-dress what they say are anti-Muslim policies.
During all the official functions held for Clinton, however, it was clear Obama would be greeted with open arms.
In his press conference with the secretary of state, Foreign Minister Hassan Wirajuda encouraged a visit.
He said Indonesia "shared the joy" of Obama's election and "cannot wait too long" for him to return to the country of his schooldays as president of the United States.
---------------------------------------------