During the 8-minute nationally televised address, Trump blamed Democrats for an 18-day partial government shutdown because of debate over the border funding proposal.
Trump said the White House issued its plan in response to the Department of Homeland Security requests for funding for technology, humanitarian needs and $5.7 billion "for a physical barrier."
The president said the proposal includes a request for technology to recognize various types of contraband, including drugs and weapons, at the border, more agents and judges to process lawful migration requests, humanitarian assistance and medical support.
He added the proposal also includes a request to close "loopholes" to return immigrant children home "safely and humanely.
Trump said the border would be made of steel "at the request of Democrats" rather than a concrete wall.
"This barrier is absolutely critical to border security," Trump said.
Trump did not declare a national emergency to secure funding for the barrier as he said he would consider last week, instead saying funding would come as a result of the United States Mexico Trade Agreement.
"The wall will also be paid for indirectly by the great new trade deal we have made with Mexico," he said.
About 25 percent of the government has been shut down, including the Department of Justice and Homeland Security, because funding hasn't been approved. Other departments, including military, are fully funded through September.
"The government remains shut down for one reason and one reason only: the Democrats will not fund border security," he said.
Trump added "situation could be resolved in a 45-minute meeting" and he invited congressional Democrats, along with Republicans, to settle the issue Wednesday. Earlier, he'll join Republican senators during their weekly lunch in the Capitol.
Schumer called on Trump to "separate the shutdown from the arguments over border security" as Pelosi noted Trump had turned down legislation passed by Congress to re-open the government without funding for a border wall.
"The president is rejecting these bi-partisan bills that would re-open the government over his obsession with forcing American taxpayers to waste billions of dollars on an expensive and ineffective wall -- a wall he always promised Mexico would pay for," said Pelosi.
Schumer agreed, saying "there is no excuse for hurting millions of Americans over a policy difference."
Pelosi added that "we all agree we need to secure our border, while honoring our values" proposing improvements to infrastructure and roads at the border, new technology to scan vehicles entering the nation, hiring personnel to facilitate trade and immigration at the border as well as funding innovations to recognize unauthorized crossings.
"The fact is the women and children at the border are not a security threat, they are a humanitarian challenge," she said.
Schumer ended the rebuttal with a call for the president to put an end to the shutdown.
"Mr. President, re-open the government and we can work to resolve our differences over border security, but end this shutdown now," he said.
About 800,00 employees have been furloughed or working without pay during the shutdown.
The president delivered the address while seeking to change the tide of public support for the wall, which is now at 38 percent, according to a December CNN poll. Roughly 57 percent of Americans oppose the border wall.
Two hours after his address, Trump posted on Twitter: "Thank you for soooo many nice comments regarding my Oval Office speech. A very interesting experience!"
All nine House members serving in districts along the border voted in favor of the bills last week that provided funding for federal agencies and reinstated Department of Homeland Security appropriations without offering any new border wall funding, CBS News reported.
Rep. Will Hurd, a Republican who represents more miles of the southern border than any other member of Congress, won a second term by campaigning against the wall and backing a technology-focused initiative he said would cost less than $1 billion.
"Tonight we didn't see anything new that we haven't already seen," he told CNN. "Unfortunately, I don't think any side put forward any initiatives that are going to move the ball forward."
The Senate on Dec. 19 unanimously approved funding the agencies through Feb. 8 without money for the wall but now Senate Majority Leader Mitch McConnell, R-Ky., won't bring the measures up because Trump changed his mind and now says he would veto them.