In a primetime address, the Republican leader said he was "extending an open hand" to Democrats to work together.
Mr Trump also said he was ordering Guantanamo Bay to be kept open, reversing an Obama-era directive to close the controversial detention camp.
The American economy is booming but Mr Trump's approval rating languishes.
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In an upbeat message a world away from his apocalyptic "American carnage" inaugural speech of just a year ago, Mr Trump said his administration was "building a safe, strong and proud America".
"There has never been a better time to start living the American dream," he told lawmakers in a one-hour-and-20-minute speech.
As many as 40 million television viewers were expected to tune in as he implored the nation to come together as "one team, one people and one American family".
Mr Trump made a plea for the kind of bipartisan co-operation that has been in short supply during a turbulent first year in office.
The president, who has enraged Democrats by withdrawing protections for immigrants who entered the US illegally as children, offered an olive branch.
"Tonight I am extending an open hand to work with members of both parties, Democrats and Republicans, to protect our citizens, of every background, colour and creed."