He said migrant children were being “used as human pawns by vicious coyotes and ruthless gangs.”
The president said one third of women crossing the border were sexually assaulted on the trek to get there.
He said: “This is the tragic reality of illegal immigration. This is the cycle of human suffering I am determined to end. It’s a tremendous problem.”
Mr Trump suggested the border wall would pay for itself “very quickly” because of the current cost to the United States of illegal drugs from Mexico
He said: “Democrats in congress have failed to acknowledge the crisis. The federal government remains shut down for one reason, and one reason only – Democrats will not fund border security. This could be solved in a 45-minute meeting.”
The president said he would meet with congressional leaders at the White House on Wednesday in an attempt to “get this done”.
He rejected suggestions that building the wall was “immoral,” saying some senior politicians had walls around their own homes.
Mr Trump said that was “not because they hate the people on the outside, it’s because they love the people on the inside”.
He added: “The only thing that is immoral is for politicians to do nothing.”
The president listed a series of cases in which illegal immigrants, including members of the MS-13 gang, had committed violent crimes.
He described how “America’s heart broke the day after Christmas” when a California police officer was murdered by an illegal immigrant.
Other cases included an Air Force veteran who was raped and beaten to death with a hammer, and one in Georgia in which an illegal immigrant beheaded and dismembered a neighbour.
Mr Trump said: “I’ve held the hands of the weeping mothers and embraced the grief-stricken parents. So sad. So terrible. I will never forget the pain in their eyes and the sadness in their souls.
“This is a choice between right and wrong, justice an injustice.”
Mr Trump’s address was delivered in a soft and measured tone.
His request for $5.7 billion was immediately rejected by Democrat leaders in Congress.
Television networks allowed Nancy Pelosi, the Democrat Speaker in the House of Representatives, and Chuck Schumer, the Democrat leader in the US Senate, to briefly address the nation directly after Mr Trump.
They accused Mr Trump of “manufacturing” a crisis and being “obsessed with an expensive and ineffective wall”.
Mrs Pelosi said: “The women and children at the border are not a security threat, they are a humanitarian challenge – a challenge that President Trump’s own cruel and counterproductive policies have only deepened.
“President Trump must stop holding the American people hostage, must stop manufacturing a crisis, and must re-open the government.”
Mr Schumer said: “We don’t govern by temper tantrum. Tonight, and throughout this debate and his presidency, President Trump has appealed to fear, not facts. Division, not unity.
“Most presidents have used Oval Office addresses for noble purposes. This president just used the backdrop of the Oval Office to manufacture a crisis, stoke fear, and divert attention from the turmoil in his Administration.
“The symbol of America should be the Statue of Liberty, not a thirty-foot wall.”