"It is clear that Mr (Malcolm) Turnbull and his coalition will form a government," Shorten told reporters in Melbourne.
"So I have spoken to Mr Turnbull earlier this afternoon to congratulate him and (his wife) Lucy and to wish them my very best."
Both Turnbull's ruling Liberal/National coalition and Labor remain short of the 76 seats needed to claim a majority in the 150-seat House of Representatives, with counting still ongoing.
The coalition is currently expected to secure 74 seats, and potentially two more, according to national broadcaster ABC's projections.
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Labor has won 66, and with five independents elected, the opposition does not have sufficient seats to govern in Canberra, according to the projections.
The two seats the coalition believe it will pick up are among five still in the balance.
Turnbull lost the government's comfortable majority in the House of Representatives in last Saturday's election after his campaign on "jobs and growth" and "innovation" failed to resonate equally across the vast island continent.
Turnbull became the nation's fourth prime minister since 2013 when he rolled Liberal leader Tony Abbott in a party vote last September.