Prime Minister Atal Behari Vajpayee resigned on Thursday to President Abd al-Kalam, who asked him to remain as caretaker premier until a new government is formed.
"We accept the people's mandate with all politeness," said Venkaiah Naidu, president of Vajpayee's Bharatiya Janata Party (BJP), which had been confident of securing a new term in the early election.
The Congress party, led by Sonia Gandhi, the Italian-born heir to India's most famous political dynasty, said it will ask Abd al-Kalam, the ceremonial head of state, to let it form a new government.
Congress, which left power in 1996 after ruling India for 45 years, was to meet late on Thursday to decide on its choice for prime minister with many pushing for Gandhi, the 57-year-old widow of slain former premier Rajiv Gandhi.
Gandhi campaign proved to be successful by appealing to the rural poor.
"All the workers want it, party officials want it. Now she will have to decide whether she wants to be the prime minister," Patel said.
Voting was largely peaceful
throughout the country
Opposition groups systematically denounced Gandhi during the campaign, saying she was still a foreigner even if she only ever appears in Indian dress and speaks in fluent, if accented, Hindi.
With 465 of the 543 seats declared by the Election Commission, Congress and its allies had won 190 seats compared with 164 for Vajpayee's Bharatiya Janata Party (BJP) and its partners.
The balance will be held largely by populist regional parties whose support will be crucial for a stable government.
Election call backfires
The BJP, which has led coalitions since 1998 as the first avowedly Hindu party to rule secular India, called the election five months ahead of schedule to capitalise on 79-year-old Vajpayee's popularity and booming economic growth.
Supporters of the Congress Pary
celebrate Gandhi's win
But Congress turned the BJP's "India Shining" re-election slogan on its head, portraying the BJP's slick campaign which included mobile telephone messages to voters as out of touch with millions of rural poor who lack proper electricity and water.
"The economic policies of BJP, which did achieve many things they had set out to achieve, alienated much of the electorate which are much too poor and marginalised to benefit from them," said political analyst Pran Chopra.
"It has cost it the support of a very large section of the population. The sympathy and concern for the hardships of the poor were not reflected in the BJP's policies," he said.
India's historic rival Pakistan expressed hope that the new government will proceed with a dialogue between the two countries initiated last year by Vajpayee, who declared he was on his last bid to make peace in South Asia.
Congress spokesman Anand Sharma told AFP the party "is committed to working towards creating lasting peace in the region."
At the headquarters of Congress, which led India to independence from Britain, a huge balloon shaped as an open palm, the 119-year-old party's symbol, dropped to the ground as supporters lit firecrackers.
"Long live Congress! Down with the BJP!" they shouted.
Sonia and Rajiv's son, Rahul Gandhi, on Thursday became the fourth-generation MP from the dynasty.
The 33-year-old former financial consultant, who spent much of his 20s in Britain and the United States, won from the family's stronghold Amethi in Uttar Pradesh.
More than 370 million people voted in the national election, held on five dates from 20 April to allow poll workers, police and soldiers to fan out to the nearly 687,500 voting stations.
Little violence was reported during the vote, despite a boycott by separatists including in Muslim-majority Kashmir.