DUP leader Ian Paisley has said good progress is being made on a number of fronts in his talks with the government over the return of devolution.
DUP leader Ian Paisley met NI Secretary Peter Hain
After meeting with NI Secretary Peter Hain, he said the abolition of water charges was achievable.
Mr Paisley and Sinn Fein leader Gerry Adams will hold separate talks with Prime Minister Tony Blair on Wednesday.
The newly elected Northern Ireland Assembly has been meeting for the first time on Tuesday at Stormont.
The 108 members were asked to sign the register and select a voting designation, either unionist, nationalist or other.
The Alliance Party announced their seven assembly members would be forming a "coherent opposition group" with the Green Party's Brian Wilson and independent MLA Dr Kieran Deeny.
The parties have until 26 March to agree a power-sharing executive or the British and Irish governments say they will shut the assembly and stop the pay of its members.
On Wednesday, the DUP leader and Sinn Fein leader Gerry Adams will hold separate meetings with Prime Minister Tony Blair.
Mr Paisley said the DUP's election success allowed him to move forward, despite the fact that he had been "severely criticised by various people".
"Some of them are my personal friends but they don't agree with what I've done, (but) the electorate fortunately has agreed," he said.
"It has strengthened my hand - I can afford to go further forward now with things, because I am confident that the people are with me."
The DUP leader also said he hoped to have a private conversation with Chancellor Gordon Brown about the likely shape of a peace dividend while he is in London on Wednesday.
The new assembly is comprised of 36 DUP members, 28 Sinn Fein members, the UUP has 18 and the SDLP has 16.
The 108 MLAs had to say if they were unionist, nationalist or other
If a power-sharing executive is formed it will have four DUP ministers, three Sinn Fein, two UUP and one SDLP.
There are new faces on the benches, including Alliance's Anna Lo, the first member to come from an ethnic minority background.
The outgoing speaker, Eileen Bell, is expected to remain in place until a replacement is elected.
The Northern Ireland Assembly has been suspended since October 2002, amid allegations of an IRA spy ring at Stormont. A subsequent court case collapsed. Direct rule has been in place since that date.
Meanwhile, the government has set out proposals for Irish language legislation in Northern Ireland.
The proposals, which will be put out to consultation, include the appointment of an Irish language commissioner and the establishment of Irish language schemes for public bodies.