The government's razor-thin majority in the House of Representatives is a recipe for instability and backbenchers will be able to hold the government to ransom, Opposition Leader Bill Shorten has claimed.

Mr Shorten said the rejection of former prime minister Kevin Rudd's bid to be the next United Nations secretary-general was a case of Prime Minister Malcolm Turnbull, in a tight Parliament, being "held hostage to his right-wing puppet masters pulling the strings".

"Before the election, the LNP, the Liberals, had 90 seats in the Parliament. Now they are reduced to a margin of one vote. That means Mr Turnbull is on probation from his backbench," Mr Shorten said.

"It means stability in Australia depends on Mr Turnbull keeping the goodwill of individuals such as the erratic member for Dawson, Mr [George] Christensen and others. What Labor offers today ... is we will be constructive in the new Parliament. That is what Australians want to hear."