Allies of India's Congress Party have voted unanimously to support Sonia Gandhi as the next prime minister.
Mrs Gandhi is expected to be sworn in this week
The party, led by Mrs Gandhi, is trying to put together a coalition government following its surprise election victory last week.
Several communist parties, which hold the balance of power, are still deciding whether to join the new government or support it from outside.
Congress won most seats in the election but fell short of a majority.
The largest left-wing party, the Communist Party of India (CPIM), is due to meet again on Monday to decide whether to accept an invitation to join a coalition.
"The question is, should we extend support [to] the government from outside, or should we also be part of it," said party leader A B Bardhan.
Correspondents say the decision is likely to depend on what policy concessions it can extract from the Congress Party.
Several parties met at Mrs Gandhi's home on Sunday night and agreed to back her as prime minister, said Congress spokesman Manmohan Singh.
Mrs Gandhi is expected to be sworn in later this week. The Italian-born widow of assassinated former Prime Minister Rajiv Gandhi will become the fourth member of the Nehru-Gandhi dynasty to hold the premiership.
Mrs Gandhi was mobbed by MPs and showered with flowers when she arrived at the parliamentary building on Saturday, after being named Congress' new parliamentary leader.
"We are all aware that we have an enormous task ahead of us," she said.
"The way ahead is fraught with difficulties. Let us therefore not be complacent."
In her first post-election interview on Friday, Mrs Gandhi said she was pleased that her Italian heritage had not harmed Congress in the polls.
"Most of the Congress Party's opponents used this against me, but I had full faith in the judgement of the people of my country," said Mrs Gandhi, who took Indian citizenship in 1983.