Turnbull's Liberal-Nationals are expected to win 76 seats, the minimum for a majority, while the opposition Labor party is predicted to win 69, the ABC said.
Independents and small parties have secured five seats in the parliament's lower house and have won key Senate seats.
Counting is continuing in some closely-fought contests and a final declaration may take several more days, leaving Turnbull the hard task of uniting a divided parliament in order to pass legislation.
Industry Minister Christopher Pyne said the coalition had a clear mandate to deliver on its election promises.
"Whether you win a grand final by one goal or six goals, a win is a win," Pyne told ABC radio.
Moody's Investors Service on Monday joined Standard and Poor's in expressing concern that a splintered upper house Senate would stymie agreement on fiscal consolidation and macroeconomic policy.
Moody's said such a scenario would be "credit negative", echoing S&P's decision last week to cut Australia's credit rating outlook to negative from stable, threatening a downgrade of its coveted triple A status.
The make-up of the Senate, where the government requires support for legislative changes, is still unclear. However, small parties run by the far-right politician Pauline Hanson and centrist Nick Xenophon are on track to win several positions, making them a force in Australia's next parliament.
Some conservative members of the Liberal Party blame their centrist leader for a loss in votes that left them perilously close to conceding power, putting pressure on Turnbull to reverse unpopular policies like changes to state pensions.
The junior coalition partner, the Nationals, meanwhile, are agitating for an extra seat in cabinet given they are on track to increase their representation in parliament.
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