Liberal senator Jane Hume also hopes incoming prime minister Anthony Albanese can form a majority Labor government, saying a hung parliament would be dysfunctional.
Mr Morrison conceded defeat on Saturday night with Labor projected to hold 77 seats in the 151-seat parliament.
The coalition is projected to hold 59 seats, with as many as 15 crossbenchers including four Greens MPs, according to election analyst William Bowe.
However, as vote counting continued the Australian Electoral Commission officially listed Labor as holding 75 seats and the coalition 51, with 12 crossbenchers and the remaining undecided.
Labor could still fall short of a majority, meaning it would need crossbench support to govern as it did between 2010 and 2013.
"I think there is a bit of counting to go, and we are hopeful that we can achieve a majority in our own right," Mr Marles told ABC's Insiders program on Sunday.
"The point that we've made all through the campaign is that what we are taking to the Australian people is what we will take to the parliament, so there is not going to be any deals in forming government."
Senator Hume conceded the so-called teal independents had an "incredible night".
"I am desperately hoping though there is not a hung parliament, I hope that it is in fact a Labor government," the outgoing financial services minister told Sky News on Sunday.
"A hung parliament is dysfunctional and won't serve the country well."
Nationals leader Barnaby Joyce, who is stepping down as deputy prime minister, said Mr Albanese has a "mighty task" in front of him to make Australia as strong as possible.
Asked if he would continue at Nationals leader, Mr Joyce said: "That's a decision for the party room."
Mr Albanese is expected to be sworn in on Monday, along with senior members of his cabinet, before heading to Tokyo for the Quad meeting with the leaders of Japan, the US and India.
Mr Morrison is set to remain in parliament, having retained his Sydney seat of Cook, but will step down as leader at the next Liberal partyroom meeting.
He and his family left Kirribilli House, the prime minister's official residence in Sydney, on Sunday morning.
Labor's primary vote of 32 per cent was lower than it achieved when the party lost the 2019 election, while the coalition scored 35 per cent.
"That says a lot about the upheaval that's taking place in our nation and I think it is important for our nation to heal and to move forward," Mr Morrison said in his concession speech on Saturday night.
Mr Albanese, who has made much of his childhood in social housing, being brought up by a single mum, said he hoped his life's journey inspired other Australians to "reach for the stars".
"I want Australia to continue to be a country that - no matter where you live, who you worship, who you love or what your last name is - places no restrictions on your journey in life."
The final result of the half-Senate election is yet to be determined, but veteran One Nation leader Pauline Hanson is not expected to be returned in Queensland.
And for the first time in the ACT's history, it is expected the Liberals will not pick up a Senate seat with independent candidate and former Wallaby David Pocock tipped to defeat outgoing minister Zed Seselja on preferences.
