The US President was speaking before Congress for the first time since Republican took control of the house of Representatives last month.
While he acknowledged that America’s democracy is bruised, Mr Biden stressed it is “unbowed and unbroken”.
The Democrat said “there is no reason we can’t work together in this new Congress” – and Americans crave unity.
He added: “The people sent us a clear message. Fighting for the sake of fighting, power for the sake of power, conflict for the sake of conflict, gets us nowhere … We’ve been sent here to finish the job!”
This annual speech gives the president an opportunity to set out their legislative priorities for the year ahead.
Mr Biden has appealed for bipartisan efforts on cancer research, supporting veterans, and beating the “opioid and overdose epidemic”.
But some of his other proposals – such as a minimum tax for billionaires – are unlikely to be passed by the current Congress.
And the president’s wish for a nationwide cap on the cost of insulin, meaning diabetes patients wouldn’t pay more than $35 (£29) a month, may not get congressional approval either.
Among those who are uninsured, the cost of insulin can be up to $900 (£746) a month – forcing many to ration or skip doses and endanger their health.
Elsewhere in the speech, Mr Biden focused on policing reform following the death of Tyre Nichols, a black man who died after being beaten by officers in Memphis. He paid tribute to Mr Nichols as his parents watched from the audience.
The White House and new Republican House Speaker Kevin McCarthy have been at loggerheads over America’s $31.4trn (£26trn) debt ceiling, which needs to be raised in the coming months to avoid a default.
In a video ahead of the State of the Union, Mr McCarthy said he respects the Democrats but has the right to disagree on policy.
He added: “I want to make sure this country is stronger, economically sound, energy independent, secure and accountable.”
Mr McCarthy also cautioned Mr Biden against using the term “extreme MAGA Republicans” in his address – a nod to Donald Trump’s “Make America Great Again” slogan.
A recent Reuters/Ipsos opinion poll put Mr Biden’s approval rating at 41%, which is close to the lowest level of his presidency.
Right now, 65% of Americans believe the country is on the wrong track, compared with 58% a year ago.
Like the UK, the US has also been suffering from red-hot levels of inflation in recent months – but the Federal Reserve is expecting “significant declines” throughout 2023.
Mr Biden’s speech was designed to set an optimistic tone ahead of a second presidential campaign in 2024, which is expected to launch in a matter of weeks.
He turned 80 years old in November and would be 82 if re-elected for a second term – and recent polls suggest this is a cause for concern among many Democratic voters.
Arkansas Governor Sarah Huckabee Sanders, who previously served as Donald Trump’s press secretary, delivered the Republican response to Mr Biden’s speech.
In a blistering attack, she claimed Mr Biden was “unfit to serve as commander-in-chief” – and claimed his administration was more interested in “woke fantasies than the hard realities Americans face every single day”.
She said the Republicans were for freedom, while the Democrats favoured government control.
“Biden and the Democrats have failed you. They know it, you know it, and it’s time for a change,” Ms Huckabee Sanders said
She warned that the right and left no longer divides the US – and now, “the choice is between normal or crazy”.
“President Biden inherited the fastest economic recovery on record; the most secure border in history; cheap, abundant homegrown energy; fast rising wages; a rebuilt military, and a world that was stable and at peace. But over the last two years, Democrats destroyed it all,” Ms Huckabee Sanders claimed.
And criticising Mr Biden’s record, she added: “Beyond our border from Afghanistan to Ukraine, from North Korea to Iran, President Biden’s weakness puts our nation and the world at risk. And the president’s refusal to stand up to China, our most formidable adversary, is dangerous and unacceptable.”