JAKARTA, Indonesia – An American-trained former general who led the fight against Al Qaeda-linked extremists in Indonesia appeared headed for a landslide victory yesterday in a presidential runoff heralded as a key step for democracy in the world’s most populous Muslim nation.

Susilo Bambang Yudhoyono, who focused his campaign on fixing the economy and cracking down on corruption, had nearly 59% of the votes in early returns. The incumbent president, Megawati Sukarnoputri, had 41%.

The General Election Commission said about 20 million votes had been counted by late yesterday, from a turnout estimated at 147 million to 152 million voters.

The Washington-based National Democratic Institute, the international arm of the Democratic Party, said its “Quick Count” survey gave Mr. Yudhoyono 61% and Megawati 39%. The group, which based its forecast on counts at selected voting stations, accurately predicted the results of Indonesia’s parliamentary elections in April and the first round of the presidential election in July, in which Mr. Yudhoyono and Ms. Megawati were the two leaders.

Mr. Yudhoyono declined to formally claim victory late yesterday, but told reporters: “I am grateful to God, and thankful to the people of Indonesia who have given me…that kind of support.”

Ms. Megawati, who had stabilized the economy but saw her popularity wane because of anger over continuing graft, did not concede, saying she would await the announcement of official results in early October.

The election was held to choose Indonesia’s fourth head of state since widespread street protests over an economic slump forced an end to the 32-year dictatorship of former military leader Mr. Suharto in 1998.

The polls were free of violence and accusations of fraud in a further boost to an orderly succession in Indonesia that is being held up as evidence that democracy can prosper in the Muslim world, most of which is ruled by authoritarian regimes.

While Mr. Yudhoyono appealed to Washington because of his hard line against terrorists in this strategically located nation that stretches under Southeast Asia from the Pacific to the Indian Ocean, most Indonesians were concerned about the economy and corruption.

The 55-year-old retired soldier said his priorities are building up an economy that is growing much slower than Indonesia’s neighbors, attacking graft and providing jobs for the country’s 210 million people.

But he also promised to crack down harder on Jemaah Islamiyah, a group with links to Al Qaeda that has been blamed for three bloody terror attacks – the September 9 truck bombing outside the Australian Embassy, last year’s bombing at the Marriott hotel in Jakarta, and the 2002 bombings in a nightclub district on the resort island of Bali.

As security minister under Ms. Megawati, Mr. Yudhoyono oversaw a campaign that is thought to have dispersed Jemaah Islamiyah’s members, forcing them to split up into smaller groups with less coordination.

“Yudhoyono is strong, caring. He is hard. He is best for Indonesia,” said Marni, a 37-year-old housekeeper who, like many Indonesians, uses only one name.

Ms. Megawati will remain a force. Her Indonesian Party of Struggle and Mr. Suharto’s former Golkar Party emerged from April’s parliamentary elections as the largest factions in the legislature, each winning about a fifth of the seats.

Mr. Yudhoyono’s new Democratic Party won just 8% of the seats, so his government will have to rely on a wide coalition of secular and moderate religious parties. But the projected size of his victory yesterday should strengthen him in dealing with Parliament.

Under Mr. Suharto, lawmakers – not voters – picked the head of state in a system the dictator abused to maintain his grip on power. Yesterday’s vote was the first time Indonesians directly elected their leader.

“I am thankful to the Megawati government for establishing this kind of democracy,” Mr. Yudhoyono said late yesterday. “I will now consolidate [my supporters] and think about the steps I can take to reconcile my camp with the Megawati camp.”

Perhaps because of his close association with her administration, Mr. Yudhoyono has refrained from criticizing Ms. Megawati or articulating alternative policies, and he was not expected to introduce radical policy shifts in Indonesia’s foreign or economic policies.

“I think we know what we’re going to get; it’ll be much of the same,” said the director of Jakarta’s Center for Strategic and International Studies, Hadi Susastro. “If he appoints credible people to help him fight corruption, that would be a good step. But I don’t think you can expect wonders or breakthroughs or major changes.”

Ms. Megawati, the daughter of the country’s founding President Sukarno and Indonesia’s first female president, was once seen as an icon of the reform movement. Her administration succeeded in stabilizing the economy and ending the chaos that followed Mr. Suharto’s overthrow.

But her apparent lack of empathy for the problems of the poor, who formed the bulk of her constituency in elections five years ago, led to charges that she had sold out to the business and military elite.

Many also criticized the failure to rein in corruption left over from Mr. Suharto’s regime, saying it was hampering economic development by scaring off foreign and domestic investors. Indonesia is regularly ranked as one of the most graft-ridden nations in the world.

“Whoever is elected must really fight against corruption,” said a human rights lawyer, Todung Mulya Lubis, who was seen as a possible attorney general under Mr. Yudhoyono.