Kadima won 28 and Likud 27 places in the 120-seat parliament.
But the parliament has a majority among hard-line parties, making it easier for Mr Netanyahu to form the next government and take over as prime minister.
Kadima Party leader Tzipi Livni, the current foreign minister, is also trying to attract coalition partners. One possibility is a joint government. Mr Netanyahu would be prime minister, while Ms Livni and her party would receive key government ministries.
The premier-designate has six weeks to form a coalition government and win approval from the new parliament.