Ahead of his meeting, Mr Adams said his party would be pressing the government to get the assembly up and running again.
"We want to see the suspension of the institutions lifted and all of
the other institutions that are part of the joint declaration that we
negotiated, the unfinished business of the Good Friday Agreement, we want acts of completion on all of those," he said.
"We're going to press the governments to move ahead, and we're going to meet the other parties."
SDLP leader Mark Durkan said he had also told Mr Murphy he wanted the assembly reconvened sooner rather than later.
He added: "The election result makes it much more difficult for the Agreement. The Agreement is damaged by the election, but it is not destroyed."
Earlier, DUP spokesman Ian Paisley junior - who won a seat alongside his father in North Antrim - told BBC Radio 4's Today programme that it was time the British Government "wakens up to the reality" that a new deal had to be sought.
"It's dead in the water. The Agreement is over - that was the message of this election," he said.
The British and Irish Governments have insisted that the Agreement remains the only viable political framework - and is not open to negotiation.
"Northern Ireland can only be governed by an accommodation between nationalists and unionists, and that accommodation over the last five or six years has been hugely successful," he said on Saturday.
"I am not underestimating the difficulties, but I am not unhopeful that we can make progress," he added, saying that power-sharing between the hard liners had already happened "whether they talked to each other or not".
Sinn Fein secured 24 seats in comparison with the SDLP's 18 - a direct reversal of the parties' positions after the last election.
The Alliance gained six assembly places, while the three remaining seats went to a County Tyrone doctor standing on a single issue over hospital services, maverick unionist Robert McCartney and Progressive Unionist David Ervine.
The last assembly election in 1998 returned 28 Ulster Unionists, 24 SDLP, 20 DUP and 18 Sinn Fein MLAs.