The Welsh assembly's presiding officer has denied there is a "crisis" over the shape of the next assembly government.
Another assembly election may take place unless a deal is reached
A series of party meetings is taking place over the next 48 hours after Labour failed to win a majority.
Dafydd Elis Thomas said the options offered a "creative period," and he has sought legal advice on whether another election would have to be called if no deal is reached by 31 May.
However, the Wales Office said that deadline could not be stretched.
As the largest party, Labour is continuing to lead attempts to form an assembly government, with its AMs meeting again on Tuesday.
Lord Elis-Thomas had asked whether there was "some discretion" in the Government of Wales Act that a new administration had to be formed 28 days after the election
But a spokesperson for Welsh Secretary Peter Hain said: "There will be no extension to the 28-day deadline." The law states that Mr Hain must put forward a date for a new election if the first minister is not appointed by the end of May.
It is thought most Labour AMs prefer an informal agreement with the Liberal Democrats, although other possibilities, including a full coalition, are still on the table.
Plaid AMs meet on Wednesday and Lib Dem AMs and their party national executive on Thursday.
However, it is understood there is strong resistance among both Lib Dem and Plaid AMs to any deal with Labour, and there may be pressure on their leaders over the next few days to come up with an alternative.
BBC Wales has spoken to 28 of the 40 Lib Dems' constituency candidates in the election and 19 were opposed to any deal with Labour. Five were in favour and the other four declined to comment.
One senior Liberal Democrat has told BBC Wales that "all leaders have to jump one way or another within the next 48 hours".
HOW THE ASSEMBLY STANDS
Labour: 26 seats
Plaid Cymru: 15
Liberal Democrats: 6
Conservatives are saying little in public, but they regard the next 48 hours as crucial, and are waiting to see if Plaid leader Ieuan Wyn Jones will call upon them and Lib Dems to enter formal negotiations.
It is understood that both Lib Dems and Plaid are prioritising a number of issues in their talks with Labour over forming a government.
It appears that Lib Dems want to see class sizes reduced, hospital reconfiguration stopped, a system of proportional representation introduced for local government elections and measures to tackle climate change as part of any deal.
It is understood that Plaid would want a referendum on having a Scotland-style parliament in Wales, a Welsh language act and a look at a number of funding issues, such as the Barnett formula - under which Wales is funded from Westminster - council tax, business rate relief and corporation tax.
Lord Elis-Thomas told Radio Wales the options available presented "a very creative period for our Welsh politics", adding: "It is not a crisis in Wales. It is democratic engagement, it's very exciting,"
He said: "Our problem is I think we're still under the shadow of the Westminster two-party system. That is not the model of Welsh politics and we shouldn't be applying it."
"What is important to me from a constitutional point of view is that we should get a government that reflects what the people voted for."
He said: "We should raise our eyes beyond Westminster and look what happens on mainland Europe, look what happens in New Zealand and other places."
Meanwhile, former Plaid leader and honorary president Dafydd Wigley has made it clear that there is no question of "seeking Janet Ryder to stand down" so that he could take her assembly seat on the north Wales regional list.
Mr Wigley was placed second on the list amid Plaid's ruling that first spot should go to a woman. Mr Wigley said Ms Ryder had his full confidence.