Soon after Mr Trump spoke, Democrats in the House approved legislation created to end the partial government shutdown - but crucially did not give into his demand for an extra $5bn (£3.95bn) for the wall.
President Donald Trump has taken just as firm a stance not to re-open the government unless money is provided for a wall on the border.
"The fact is a wall is an immorality".
She offered the children the opportunity to go back to their families for the full House swearing-in, but many of them made a decision to remain there with her.
The bills passed by the House of Representatives would fund homeland security operations, including $1.3bn in border security, until 8 February, and fund several other agencies until September.
The president is due to resume budget talks with top Democrats and Republicans on Friday.
The bills have nearly no chance of passing the Republican-controlled Senate where Republicans say they will consider only legislation that has President Donald Trump's support.
The key sticking point in the shutdown fight is the President's demand for $5 billion in wall funding, which congressional Democrats have refused to meet.
Axios's Alexi McCammond reports that Tlaib quoted her son telling her, "Look mama you won. It's an old way of thinking, it isn't cost effective".
The first day of a new Congress is usually like the first day of school. The House and Senate were to each have a record number of female members on Thursday.More news: United States envoy meets American accused by Russian Federation of spying
Pelosi, who was elected speaker earlier Thursday, also took a shot a Trump, calling his proposal "a wall between reality and his constituents".
The first two Native American women and first two Muslim women were also elected.
While celebrating the Democratic diversity during the swearing-in ceremonies, some on social media highlighted the contrast to the Republican members, who are mostly white men.
They are all but dead on arrival in the Senate, where the Republican leadership has vowed not to bring them up for a vote because they do not pass muster with the president.
There are ideological differences between numerous newcomers and the Democratic party's establishment.
Minutes after Rep. Nancy Pelosi (D-CA) reclaimed the House speaker's gavel on Thursday afternoon, White House Press Secretary Sarah Huckabee Sanders announced that she would be holding an impromptu press briefing, giving reporters approximately five minutes to prepare. Dick Durbin and House Speaker Nancy Pelosi met with President Trump about the shutdown.
How has the shutdown come about?
Democrats wish to put an end to the partial government shutdown, but Republicans called the move "political theatre" in a new period in the Donald Trump era.
Trump himself made an appearance in the White House briefing room, where, flanked by members of the union for Border Patrol agents, he said he has "never had so much support as I have in the last week over my stance on border security. and for, frankly, the wall, or the barrier".
Referring to the November mid-term elections, in which the Democrats gained majority in the House, Pelosi said that Americans want a Congress that delivers results for the people, opening up opportunity and lifting up their lives.