However, Ulster Unionist Party leader Mike Nesbitt said Baroness Thatcher was "a colossus of conviction politics".
Roy Beggs, Ulster Unionist Party MLA for East Antrim, asked "why elderly residents weren't treated better".
The offer is contained in a letter to the Ulster Unionist Party leader Tom Elliott.
BBC: News - Conservatives want UUP to disband and form new Tory-led party
Mr McCrea has the right of appeal to the party officers of the Ulster Unionist Party.
The Ulster Unionist Party's sole executive Minister Danny Kennedy denied the party was in trouble.
After the meeting, David Trimble briefed members of his Ulster Unionist Party at a nearby hotel.
Ulster Unionist Party MLA Basil McCrea has said he will resign from the party.
However, the strategy of closer co-operation with the DUP has divided the Ulster Unionist party.
Media speculation about the talks has prompted Ulster Unionist Party chairman James Cooper to issue a statement.
The Ulster Unionist Party has confirmed that two candidates will vie for the position of party leader.
The Ulster Unionist Party and Democratic Unionist Party have also taken their seats despite opposition to some reforms.
Ulster Unionist Party Deputy Leader John Taylor hit back at Mr Mandelson's remarks, branding them a "despicable" attack.
Lagan Valley assembly member Basil McCrea has received a formal warning from the Ulster Unionist Party's disciplinary panel.
The DUP has attacked the Ulster Unionist Party for its motion, led by Tom Elliott and Mike Nesbitt.
The DUP leader also called on David Trimble to step down from the leadership of the Ulster Unionist Party.
"There is no question of the Ulster Unionist Party being dissolved, " he said.
BBC: News - Conservatives want UUP to disband and form new Tory-led party
David Trimble was the surprise winner in the race for the leadership of the Ulster Unionist Party in 1995.
The commission stemmed from demands by the Ulster Unionist Party for effective sanctions against those who breach the Agreement.
The Ulster Unionist Party, the DUP's main unionist rivals, said that Mr Robinson has weakened public confidence in devolution.
The move opens the way for another candidate to become lord mayor - probably Jim Rodgers of the Ulster Unionist Party.
He was seen more to be English rather than Ulster and that was a great disadvantage for the Ulster Unionist party.
Other parties have been pummelled at the polls: the Ulster Unionist Party has gone from ten MPs in Westminster to none.
That would enable Mr Mandelson to suspend the assembly before Saturday's crucial meeting of the ruling council of the Ulster Unionist Party.
The Ulster Unionist Party's ruling council is due to meet on Saturday.
The party formed an alliance with the Ulster Unionist Party in 2008 and put forward joint candidates in the European and general election.
BBC: News - Conservatives want UUP to disband and form new Tory-led party
In 1978 he entered mainstream unionism and joined the Ulster Unionist Party, and in 1990 he was elected as MP for Upper Bann.
But the House of Commons debate on the release of prisoners did sow genuine confusion in the ranks of the Ulster Unionist Party.
Both men have quit the Ulster Unionist Party over the decision of the party to support a unionist unity candidate in the Mid-Ulster by-election.
The two leaders will meet the three main Northern Ireland parties who support the Agreement - the Ulster Unionist Party, SDLP and Sinn Fein.
Ulster Unionist Party councillor Mark Cosgrove said a union flag protest which had been held in the area two hours earlier had been peaceful.
BBC: Five police officers hurt during rioting in Newtownabbey
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