SYDNEY, May 21 (Reuters) - Australian Prime Minister Scott Morrison conceded defeat in an election on Saturday and the opposition Labor Party was set to end almost a decade of conservative rule, possibly with the support of independents who campaigned for greener policies.

Partial results showed that while Labor had made small gains, Morrison's Liberal-National coalition had been punished by voters in Western Australia and affluent urban seats in particular.

The Greens and a group of so-called "teal independents", who campaigned on policies of integrity, gender equality and tackling climate change, put on a strong showing, tapping voter anger over inaction on climate change after some of the worst floods and fires to hit Australia. read more

The new parliament looks set to be much less climate-sceptic than the one that supported Morrison's pro-coal mining administration.

"Tonight, I have spoken to the leader of the opposition and the incoming prime minister, Anthony Albanese. And I've congratulated him on his election victory this evening," Morrison said, adding he was stepping down as leader of his party.

Albanese, speaking as he headed to his party celebrations, said he wanted to unite the country.

"I think people want to come together, look for our common interest, look towards that sense of common purpose. I think people have had enough of division, what they want is to come together as a nation and I intend to lead that."

In results so far, Labor had yet to reach the 76 of the 151 lower house seats required to form a government alone. Final results could take time as counting of a record number of postal votes is completed.

With 55% of the vote counted, Labor had 72 seats and Morrison's coalition 52. Independents and the Greens held 11, the Australian Broadcasting Corp projected. A further 16 seats remained in doubt.

The centre-left Labor had held a decent lead in opinion polls before the election, although surveys showed the Liberal-National government narrowing the gap in the final stretch of a six-week campaign.