Ramos-Horta has been pushing for a unity government, but intense and prolonged party rivalry has prevented the formation of a coalition.
On Monday, rival leaders Mari Alkatiri, the former prime minister, and Xanana Gusmao, the former president, turned up for the first session of the 65-member parliament.
Alkatiri's Fretilin party, which had been in power since East Timor's independence in 2002, won just 21 seats, while the National Congress for the Reconstruction of East Timor (CNRT) led by Gusmao won 18 seats.
Coalition proposal
The CNRT has joined forces with smaller parties to propose a coalition government with a total of 37 seats, saying it will consider going into opposition if it was unsuccessful.
Alkatiri has so far rejected any possibility of teaming up with Gusmao to form the government.
The former Portuguese colony has suffered a year of sporadic violence and political tensions since the streets of its capital, Dili, were hit by bloody riots last year that left at least 37 people dead.
Police said tensions in Dili have escalated in recent weeks with repeated skirmishes between UN police and youth gangs.
More than 2,000 UN police and peacekeepers are currently overseeing security in the country.