Trump is demanding billions of dollars to build his wall along the USA border with Mexico, which the Democrats have refused. Democrats have called the wall immoral, ineffective and medieval.
In one of the first acts of the new Congress, the House passed a short-term bill funding the Department of Homeland Security for about a month and a measure providing money for every other federal department or agency now without funding through the rest of the fiscal year, which goes through September.
However, it requires Senate approval, and sign off from the president, in order to become law.
That includes $12 billion in new money for foreign aid, $2 billion in funding Mr. Trump doesn't want to see in the Environmental Protection Agency and $7.1 billion he says isn't needed in the Housing and Urban Development Department.
Pelosi, elected speaker 220-192, took the gavel saying US voters "demanded a new dawn" in the November election that swept the Democrats to a House majority and are looking to "the beauty of our Constitution" to provide checks and balances on power.
"We're not doing a wall", Pelosi told reporters shortly before the votes largely along party lines. "It isn't cost effective", Pelosi added. He also claimed his refusal to budge was winning praise, telling reporters, "I have never had so much support as I have in the last week over my stance for border security".
Several lawmakers cheered and applauded at length when Pelosi reclaimed the speaker's gavel - a striking comeback for the only woman ever to hold the post.
After being sworn in, Crow outlined a mission of public service for himself and new congressional representatives.
House Democrats are sweeping into power this week on a campaign promise of improving government for ordinary Americans.
Democrats are flexing their muscles as the incoming majority in the US House of Representatives, introducing articles of impeachment and even quixotic constitutional amendments even though they have no hope of passing.
He went on to congratulate newly elected House Speaker Nancy Pelosi, calling her new position a "tremendous achievement".
Pelosi will preside over the most diverse Congress in history.
How has the shutdown come about?
The legislation comes 13 days after about a quarter of the United States government shut down and on the first day of a Democrat-controlled House.
After the opening session of the 116th Congress in which Pelosi was elected as speaker for the second time in her storied career, lawmakers took aim at a bipartisan priority of ending a partial government shutdown that was stretching into its 13th day. They also said years of Republican advertising painting Pelosi as an out-of-touch radical had hurt Democrats' chances to win in moderate districts. Talks are expected to resume on Friday.