Theresa May said the Government would be "bringing this country back together" as Labour was embroiled in a leadership battle.
Jeremy Corbyn asked Mrs May what she would be doing about families struggling to survive and how she would offered them "hope and security".
The prime minister responded by saying that the answer was a "strong economy", adding that the Government was focused on "building a country that works for everyone".
She said: "The Labour Party may be about to spend several months fighting and tearing itself apart. The Conservative Party will be spending those months bringing this country back together.
Theresa May has taken her first Prime Minister's Questions before travelling to Berlin to hold "frank and open" discussions with German Chancellor Angela Merkel.
But how well do you think May did?
The prime minister made a thinly-veiled attack on Jeremy Corbyn's embattled position as Labour leader as she was challenged about "unscrupulous bosses".
Theresa May said it was "interesting" that Mr Corbyn had raised the issue of workers with job insecurity and potentially unscrupulous bosses.
"I suspect that there are many members on the opposition benches who might be familiar with an unscrupulous boss," she said to cheers from the Tory benches.
"A boss who doesn't listen to his workers.
"Maybe even a boss who exploits the rules to further his own career. Remind him of anybody?"
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Jeremy Corbyn challenged Theresa May on comments made by new Foreign Secretary Boris Johnson about Barack Obama and black people.
Mrs May said that as home secretary she had dealt with the problem of stop and search, making sure no one was searched because of the colour of their skin.
She said that in the 13 years of the last Labour government, "nothing" had been done about the issue.
Corbyn goes for Johnson on Obama comments. Good topical question for him.
May ignores Corbyn's good Boris question. Corbyn decides not to press her on it.
Jeremy Corbyn welcomed the appointment of Theresa May as prime minister and pointed to the fact she is the second woman to fill the post.
Mrs May responded by saying she had "long heard" Labour asking what the Conservative Party does for women.
"It just keeps making us prime minister," she said.
Theresa May welcomed today's employment figures, which showed unemployment fell by 54,000 to 1.65 million between March and May.
Conservative MPs cheered as Theresa May entered the House of Commons ahead of her first Prime Minister's Questions.
Prime Minister Theresa May has left Number 10 for the House of Commons as she prepares to face Prime Minister's Questions for the first time since replacing David Cameron.