"The people of India know what is good for them and they always make the right choice," she said.
The UPA is, however, still short of the 272 seats needed for a parliamentary majority.
The BJP-led alliance is projected to take 160 seats while the Third Front, an alliance of communist and regional parties, is set to win only 87 seats, NDTV said.
Arun Jaitley, leader of the BJP, conceded that his party had been defeated.
"The Congress has the biggest mandate ... I think if Congress wants to compliment some of its leaders in this hour of victory, I think they're entitled to do so," he said.
Prakash Karat, general secretary of the Communist Party of India (Marxist), also conceded defeat.
"We have suffered a major setback," Karat said. "This is a victory for the Congress and its allies who will now clearly form the government."
Al Jazeera's Barnaby Phillips in New Delhi said: "Congress appears to have done spectacularly well, particularly against the left and forces of the [rival] Third Front, whose supports appears to have collapsed in some areas.
"In the centre of New Delhi, outside the Congress party headquarters, supporters are out on the streets celebrating."
Sankarshan Thakur, an editor with the Kolkata-based Telegraph newspaper, said the Congress had been rewarded for pursuing policies that focused on the rural poor.
"It was a combination of luck [good monsoons that helped good crops yield] and good governance. Schemes guranteeing employment for the rural poor helped," he told Al Jazeera.
Communists in the southern state of Kerala and in the eastern province of West Bengal have put in a poor performance, handing the advantage to the Congress camp, our correspondent said.
"There have [also] been big gains for Congress in Uttar Pradesh, the most populous state in all of India, and Rajasthan, in the west [of the country]," he said.
Raj Chengappa, editor of India Today newsmagazine, said a number of factors had played a role in the success of the Congress-led combine.
"First I think [was] their entire focus on development and the economy. Congress has a very strong economic team. Second, they have shunned divisive politics, unlike the BJP," he told Al Jazeera.
"Third, we had for the first time a very young generation that is voting in large numbers. I went to a poll booth and I was surprised that almost 50 per cent of the voters were below 25. This is an unusual phenomenon. I think they rooted for Congress.
"Another factor was that rural India voted strongly for development again, because the [ruling coalition] had money in their hands; the economic meltdown had not hit [rural dwellers] as much as [those] in urban India."
Computerised counting of votes at hundreds of centres across the country began at 0230 GMT on Saturday, with the results for all parliamentary seats due later in the day.
About 714 million people were eligible to vote in the largest such exercise in the world.
The vote was staggered over a month to allow security forces and election officials to supervise it.
|Indians have kept a keen eye on the
outcome of the election [AFP]
Speculation as to the eventual make-up of the government has thrown up countless permutations but most analysts agree that the most likely outcome is a patchwork coalition that will struggle to see out a full term.
By tradition, the party winning the most seats has the first right to try to form a government.
But both Congress and the BJP are sure to make a play for power no matter which emerges as the largest single party on Saturday.
Their respective leaderships have been holding a series of strategy meetings over the past two days, with the Congress party looking to mend fences with their former communist allies and the BJP also identifying potential partners.
If the two main alliances fail to make a breakthrough, the path to power might open up for the Third Front, a loose coalition of communists and regional parties.
But such a coalition would suffer from the large number of disparate parties it would need to form a government.