They were upbeat about what they described as a "very productive" first meeting with Mr Powell.
The British and Irish governments have also called for the move which they believe would limit the splinter group's ability to raise funds in the US.
Mr Trimble was speaking after a meeting which both he and Deputy First Minister Seamus Mallon had with US Secretary of State Colin Powell on Wednesday.
They are on a three-day trip to Washington DC during which they are briefing the new American administration on the peace process.
Mr Trimble, the Ulster Unionist leader, and Mr Mallon, deputy leader of the Social Democratic and Labour Party, are now preparing for their opportunity to meet President George W Bush during a lunch in the US Congress and a reception at the White House on Friday.
They were upbeat about what they described as a "very productive" first meeting with Mr Powell.
They discussed the latest developments in the peace process, including the IRA's confirmation that it has re-started contact with General De Chastelain's international decommissioning body.
Both Mr Mallon and Mr Trimble said they wanted to hear the general's own account of his meeting with the IRA.
The lack of paramilitary disarmament is one of the issues creating a stumbling block in the peace process.
When Mr Trimble and Mr Mallon meet Mr Bush, disarmament is expected to be one of the issues they will discuss.
Following the ministers' first joint official contacts on Wednesday, Mr Trimble said the Bush administration needed to limit the supply of funds and material to dissident republicans.
He said: "The Clinton administration had started the procedure for putting the Real IRA on the state department's list of proscribed organisations.
"I expect that to be carried on vigorously by the new administration."
Paisley meeting
However, leader of the anti-Good Friday Agreement Democratic Unionist Party, Ian Paisley, has said he intends to lobby the president for a block on all Irish republican fundraising.
Mr Paisley and deputy DUP leader Peter Robinson fly to the US on Thursday.
It will be the first time they will be in the White House during the St Patrick's Day event.
However, speaking on BBC Radio Ulster, Mr Paisley said he intended to tell the president of his party's opposition to Northern Ireland powersharing, in a separate meeting from the other parties.
He said: "I don't think he would want the Oklahoma bombers forced into the government in the United States of America.
"Why should we have IRA-Sinn Fein forced on us when they haven't given up an arm or declared that they will give up their arms."
Arriving in Washington on Wednesday, Irish prime minister Bertie Ahern described the IRA move to resume contact with the arms body as a "very welcome development".
Mr Ahern is to meet President Bush and speak at an America Ireland Fund gala dinner on Thursday.
On Friday, Mr Ahern is to present a St Patrick's Day shamrock to Mr Bush.