All 108 MLAs met to sign the roll of membership, with 29 newly-elected members doing so for the first time.
The Ulster Unionists announced they will form an opposition.
UUP leader Mike Nesbitt said "let battle commence".
Mr Nesbitt, said the first and deputy first minister would not have the support of his party at the executive table, as the "Ulster Unionist MLA group have unanimously decided to form the first official opposition of this Northern Ireland Assembly".
He said: "This is a big and bold move to bring a better and a more normal democracy to the people of Northern Ireland - let battle commence!".
Mr McGuinness said Mr Nesbitt's move was "deeply disappointing" and a "huge mistake".
"It will be seen as a lack of leadership," he added.
SDLP (Social Democratic and Labour Party) leader Colum Eastwood said they have some work to do before making any decisions.
Alliance party leader David Ford congratulated Mr Nesbitt on the "sound bite of the day".
"Some of us recognise that government is a bit more substantial than the sound bite of the day" he said.
The DUP's Robin Newton has been elected as the new speaker, replacing Mitchel McLaughlin, who announced his retirement before the election.
Mr Newton said he wants to "uphold the standards that his predecessors have set".
"The people of Northern Ireland are looking to us," he added. "I want to prove to them that we are moving forward."
Sinn Féin's Caitríona Ruane, the SDLP's Patsy McGlone and the UUP's Danny Kennedy have been elected as deputy speakers.
Ms Ruane has been elected as the principal deputy speaker.
People Before Profit Alliance MLAs Eamonn McCann and Gerry Carroll were among the newly-elected members signing the roll.
Mr Carroll revealed via social media that when they were asked to designate as "unionist, nationalist or other", he and Mr McCann wrote "socialist".
"We will be put in the 'other' camp, but we are clear where we stand," he said.
"This isn't the Alliance Party. This is the new socialist alternative."
MLAs also undertook to support the rule of law, challenge paramilitary activity and accept no authority but a democratic mandate.
Live coverage of proceedings at the new NI assembly
The full Northern Ireland Executive will be formed when a programme for government has been agreed.
The parties, who were given an outline of a framework for government programme on Tuesday, have until Thursday to make a response.
Negotiations on the framework could go on for two weeks.
In last week's election, the Democratic Unionist Party maintained the 38 seats it held in the last assembly, while Sinn Féin lost one and now holds 28.
The Ulster Unionists have 16 seats, while the Social Democratic and Labour Party lost two and now have 12.
The Alliance Party secured eight seats during the election, meaning it does not have enough seats to automatically qualify for a ministerial department.
The DUP's Arlene Foster has been reappointed as Northern Ireland first minister and Sinn Féin's Martin McGuinness as deputy first minister, with the UUP announcing they will form an opposition at the Stormont assembly.