They began sparring after Acosta asked Mr Trump about the caravan of migrants heading from Latin America to the southern United States border.
The Republican president also clashed repeatedly with reporters at the White House, ordering them to be quiet.
Trump had worked hard to ensure neither chamber fell to the Democrats, holding a campaigning blitz in the run-up to Tuesday's polls that saw him traverse the continental U.S. Democrats were able to ride opposition to Trump to wins in more Democratic-leaning states like NY and deep-red states like Oklahoma.
He suggested they could co-operate on issues such as infrastructure, trade and health. Likewise, the 2006 election, considered a referendum on George W Bush's war on terror and unpopular foreign policies, delivered a thumping victory for Democrats who regained both Houses of Congress.
Democratic Rep. Jerrold Nadler, who is slated to steer the House Judiciary Committee warned that the election was about accountability for Trump.
Trump's comments come ahead of his scheduled news conference Wednesday morning. At the same time, there could be regular reports about what the committee staff has found in subpoenaed records - perhaps Trump's tax returns, his company's internal financial documents, the records of his various oligarch partners in the former Soviet Union, and e-mails and other digital messages between Trump's team and people in Russian Federation.
Rep. Eric Swalwell (D-Calif.), a member of the House Intelligence Committee, promised to pursue Trump's tax returns for the sake of transparency and to reveal any potential corruption. Democrats also won in Indiana, Missouri and North Dakota: states Trump won by large margins in 2016.
Trump said that he was considering changes to his administration in the aftermath of the election, including to his cabinet.
In ill-tempered exchanges, he called a CNN correspondent "a rude, awful person" and told an NBC reporter: "I'm not a big fan of yours either". "The president was very helpful to us".
Mr Trump told a black reporter who asked whether his self-professed nationalism would embolden white nationalists that it was "such a racist question".
U.S. Issues Emergency Directive After Jet Crash in Indonesia
The AD requires flight crew to comply with a runaway stabiliser procedure in the Boeing operating procedures manual. In December 2014, an AirAsia flight from Surabaya to Singapore plunged into the sea, killing all 162 on board.
Trump forced Attorney General Jeff Sessions to resign.. -Mexican border, the handling of last year's Hurricane Maria crisis in the island territory of Puerto Rico, and alleged conflicts of interest between Trump's businesses and his presidency.
Early on Wednesday, Mr Trump added: "Now we can all get back to work and get things done!"
Previous presidents who have suffered mid-term setbacks have professed humility and said they learned valuable lessons.
All 435 seats in the U.S. House were up for re-election, although fewer than 90 were considered competitive.
John McCain, nominally a Republican, for contributing to the GOP's losing the House. Republican Sen. Dean Heller of Nevada, for example was defeated although he had embraced Trump, with both highlighting their desire to get more of the president's judicial nominees confirmed, a top priority for many social conservatives.
Trump's Republicans lost the House of Representatives in Tuesday's vote but increased their majority in the Senate.
Joining Davids as one of the first Indigenous women elected to Congress was fellow Democrat Deb Haaland, a member of the Laguna Pueblo tribe who will represent New Mexico's first district.
Some Democrats said during their campaigns that they would not back Pelosi, but it's not clear yet whether there are any Democrats willing to challenge her for the post. Republicans in this midterm benefited from having only nine seats up for grabs in the senate, compared to 26 for Democrats and the Independents who caucus with them.
"Today is more than about Democrats and Republicans".
The news for the next year or longer seems likely to be dominated by a steady stream of coverage of the people closest to Trump as they testify before Congress under duress, or under a grant of immunity, or coverage of their refusal to speak at all for fear of incriminating themselves.