There "could be a beautiful bipartisan situation," he said on Wednesday citing infrastructure tax cuts for the middle class and healthcare as areas where they could work together.
He welcomed the offer to work across the divide by Democratic Party leader Nancy Pelosi, who is likely to reclaim speakership. She had had said, "We will have accountability and strive for bipartisanship."
At the same time, Trump said that if the Democrats took a "warlike approach" to investigating him, he would respond in kind unleashing counter probes.
Criticised for backing out of the Paris climate change agreement, he even said, "Environment is very important to me."
But he added that he would not do anything on climate change that would affect the US jobs or the economy.
On immigration, he said that "we need people coming to the country," but they have to come in legally.
With companies relocating to the US and the economy expanding, the US needed more legal immigrants, he added.
But it was questions about immigration that brought the rift with the media to the fore.
Reporters' questions about him calling a caravan of several thousand Central Americans marching to the US "invaders" and airing advertisements portraying illegal immigrants scaling the border barriers, brought an angry response that he believed they were invaders.
As a reporter persisted, Trump accused the reporter and the media of being hostile to him.
Repeating his controversial statement, he said, "When you report fake news you are enemy of the people.
Trump denied that the loss of the House of Representatives was a defeat for him and compared his performance to that of his predecessor Barack Obama.
He boasted about the Republicans picking up two Senate seats -- and possibly three -- while in 2010 the Democrats lost six, and said that his party lost only 27 House seats versus the 63 lost by Democrats during Obama's midterm.
(Arul Louis can be reached at firstname.lastname@example.org and followed on Twitter @arulouis)