The president spoke at the White House Rose Garden and said a deal had been made with congressional leadership to reopen the government for three weeks.
“I am very proud to announce today that we have reached a deal to end the shutdown and reopen the federal government,” Mr Trump said from the Rose Garden.
The deal will keep the government open until 15 February while negotiations continue over funding for the border wall.
In his rambling address the president said: “Barrier or walls will be an important part of the solution.”
Mr Trump said a bipartisan committee of lawmakers would be made to consider border spending before the new deadline.
“They are willing to put partisanship aside, I think, and put the security of the American people first,” Trump said.
The breakthrough came as LaGuardia Airport in New York and Newark Liberty International Airport in New Jersey both experienced at least 90-minute delays in take-offs due to the shutdown.
Follow events as they happened below
Additional reporting by Associated Press
Hello and welcome to this liveblog, where we will be bringing you all the latest updates regarding the situation at LaGuardia airport.
Republican and Democratic leaders searched for a way to halt the 35-day partial government shutdown on Friday, but remained at odds over President Donald Trump's demand that any compromise include money for his coveted border wall.
"There are discussions on the Senate side. We are in touch with them," House Speaker Nancy Pelosi told reporters Friday morning as she entered the Capitol. Asked about Trump's demands for border security measures as part of a bill temporarily reopening government, Pelosi said, "we'll see what happens today. One step at a time."
New York Governor Andrew Cuomo says the federal government shutdown is impacting safety and security at airports and putting travelers at risk.
The Democrat wrote to Republican President Donald Trump on Friday demanding that he reopen government immediately. He said the partial shutdown is reducing staffing for Transportation Security Administration workers as well as air traffic controllers. He noted an increase in the number of TSA workers calling in absent, and said many air traffic controllers are working extra shifts without pay.
Cuomo's letter was announced shortly before the FAA announced LaGuardia Airport in New York and Newark Liberty International Airport in New Jersey were both experiencing delays in takeoffs due to staffing problems at two East Coast air traffic control facilities.
The Federal Aviation Administration is reporting delays in air travel because of a "slight increase in sick leave" at two East Coast air traffic control facilities.
FAA spokesman Gregory Martin said Friday that it had augmented staffing, rerouted traffic and increased spacing between planes as needed.
The staffing problems were at air traffic centers in Jacksonville, Florida and a Washington, DC. center that controls high-altitude air traffic over seven states.
Martin says safety is being maintained during a period of "minimal impacts" on travel.
LaGuardia Airport in New York and Newark Liberty International Airport in New Jersey were both experiencing delays in takeoffs.
Pressure is building among both parties to reopen agencies immediately and pay hundreds of thousands of beleaguered federal workers while bargainers hunt for a deal.
But the idea has not been endorsed by Trump, who says any short-term deal must include a large down-payment for a border wall — an idea House Speaker Nancy Pelosi and Minority Leader Chuck Schumer have rejected.
At the White House Thursday, Trump told reporters he'd support "a reasonable agreement." He suggested he'd also want a "prorated down payment" for his long-sought border wall with Mexico but didn't describe the term. He said he has "other alternatives" for getting wall funding, an apparent reference to his disputed claim that he could declare a national emergency and fund the wall's construction using other programs in the federal budget.
On Friday, White House Press Secretary Sarah Sanders didn't offer much clarity.
"I'm not going to negotiate in the press, but we've laid out a proposal of not what we want, but what the people and the professionals at the border say that they need to do their jobs," Sander said. "And that's what the president wants to see happen. And we are going to work to get there one way or another."
Several social media users have shared quips about LaGuardia, implying that the New York City airport already faced more than enough issues prior to the shutdown.
The Federal Aviation Authority briefly issued a ground stop for arriving flights at New York's LaGuardia Airport on Friday morning as the government dealt with staffing shortages at two air traffic control facilities in New York and Florida.
The FAA issued a notice that it was halting flights into LaGuardia due to staffing issues, but lifted it around 10:45 a.m. The FAA said it was instituting a program to manage traffic that would result in significant delays for arriving flights of nearly 90 minutes.
"We've mitigated the impact by augmenting staffing, rerouting traffic, and increasing spacing between aircraft as needed," the FAA said. "The results have been minimal impacts to efficiency while maintaining consistent levels of safety in the national airspace system."
Controllers and airport screeners are not being paid during the ongoing government shutdown that has reached 35 days.
On Thursday, three major US airlines – American Airlines Group Inc, Southwest Airlines Co and JetBlue Airways Corp – said the impact of the shutdown on their business had so far been limited but was nearing a tipping point.
"No one can predict what impact it will have as it continues," Southwest Chief Executive Gary Kelly said of the shutdown on Thursday.
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