However several smaller parties, whose support Ms Livni would need, are opposed to some of her policies, especially her pledge to exchange land for peace with the Palestinians.
Final results are expected within days.
BBC diplomatic correspondent Jonathan Marcus says the closeness of the forecast result is in many ways the worst outcome for Israeli democracy, as it sets the scene for days and probably weeks of fractious political horse-trading.
Once final results are in, President Shimon Peres will consult party leaders to determine who among them stands the best chance of forming a coalition government, but he does not have to nominate the leader of the largest party.
Supporters of Kadima celebrated when the exit polls were released
Whoever is chosen then has up to 42 days to form a coalition. If the attempt fails, Mr Peres can ask another leader to assume the task.
The election has been dominated by security issues following Israel's offensive in the Gaza Strip controlled by the Palestinian militant group Hamas.
Although its rival in the West Bank, the Palestinian Authority, has not expressed preference for any candidate, senior negotiator Saeb Erakat expressed dismay right-wing parties that oppose the traditional land-for-peace formula had performed so well.
"It is obvious the Israelis have voted to paralyse the peace process," he said.
In Kuwait, French president Nicolas Sarkozy said he hoped Israel's new leadership would "have an obsession with peace... which is the guarantee of Israel's security," AFP quoted him saying.
Elections were called early after Ms Livni failed to form a new government following Prime Minister Ehud Olmert's decision to step down last year amid a corruption probe against him.
Mr Olmert will stay on as caretaker prime minister until a new government is formed.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.