The separatist Democratic Party of Kosovo of Hashim Thaci, the former rebel leader, won most seats in November elections, but fell short of winning enough to rule outright.
Thaci, who is expected to become prime minister, has yet to strike a power-sharing deal with the party's main political rival, the Democratic League of Kosovo of the late pacifist leader Ibrahim Rugova, which came second in the poll.
Both parties back statehood for Kosovo, but in the absence of any deal, politicians postponed the election of a speaker until next week.
Speaking after the inaugural session, Thaci said: "This is the beginning of a new year, with a new leadership and a new vision, of a parliament and all institutions of an independent Kosovo."
After winning the November elections, Thaci had said he would swiftly declare independence, but in the following days he said any such move would be coordinated with the United States and the European Union to allay international fears about instability in the region.
He repeated his pledge on Friday, saying Kosovo's leadership was "determined to work together with international partners in making Kosovo's independence and sovereignty official".
Western diplomats favour a broad political coalition which they see as a guarantee of stability among ethnic Albanians as the move towards the anticipated declaration of independence comes closer.
However, no move is likely to take place before presidential elections in Serbia set for January 20.
Serbia, backed by Russia, insists that Kosovo, which is considered the cradle of Serbia's medieval state and religion, should remain part of its territory.
The US and several EU nations have said that they would recognise Kosovo's independence because it has not been under Serbia's control since 1999, when Nato intervened to stop a Serb military crackdown on ethnic Albanian separatists.
Last year, international envoys failed to resolve the issue of whether Kosovo should become independent or remain part of Serbia, and the dispute will now go back to the UN Security Council.
Russia has previously threatened to veto any measure that allows Kosovo to become a state.
Thaci, 39, was leader of the now disbanded Kosovo Liberation Army that waged an independence war against Serbia in 1998 to 1999.
Most of his associates are former fighters and are expected to take senior positions in the future government.