UPDATE 2-Australia to build $31 bln broadband network

* Private-public project to cost A$43 bln ($31 bln)

* Govt to sell majority stake after five years

* Scheme will be country's largest infrastructure project * Project will support 37,000 jobs

* Telstra shares up 4 percent (Adds details)

By Rob Taylor

CANBERRA, April 7 (Reuters) - Australia's government will build a A$43 billion ($30.7 billion) national high-speed fibre-optic broadband network, rejecting bids in a controversial tender involving some of the country's top telecoms firms.

In a surprise decision, Prime Minister Kevin Rudd said on Tuesday the government would ask private companies join a new private-public firm to build the network.

The government would sell its majority stake after five years when the network was fully operational.

The government had been expected to announce the winner of the tender to build the network, which was a centrepiece of Rudd's winning election campaign in late 2007.