Turnbull reaches out to Abbott supporters

Conservative government MPs who did not back the leadership change to Malcolm Turnbull are putting on a brave face as they return to Canberra.

Liberal senator Zed Seselja says Tony Abbott supporters are putting the spill behind them and have been having some "positive" discussions with Mr Turnbull.

"There's an overwhelming mood that we want to see the government succeed," he told ABC radio on Monday.

Mr Turnbull invited coalition MPs to a barbecue in the prime minister's courtyard on Sunday night ahead of parliament sitting for the next fortnight.

Northern Territory MP Natasha Griggs said her electorate wants her to work with the new leader.

"I can absolutely work with the current cabinet. There's a lot of fresh faces in there," she told ABC radio.