President Barack Obama appears on "The View" at ABC Studios in New York on Monday.

Story highlights

NEW: Obama promotes theme of "togetherness" at a fundraiser

Obama tells Barnard grads they can "shape ... the destiny of this nation and of this world"

He encourages graduates to "speak up for what's right"

His commencement speech comes days after Mitt Romney's Liberty University speech

CNN  — 

President Barack Obama touched on his recent announcement of support for same-sex marriage, saying at a New York City fundraising event Monday that he believes marriage equality “strengthens families.”

“I want everyone treated fairly in this country. We have never gone wrong when we’ve extended rights and responsibilities to everybody,” he said, drawing big applause. “That doesn’t weaken families, that strengthens families.”

Obama highlighted some of his administration’s work in recent years, including the passage of health care reform and the end of combat in Iraq.

He also outlined goals he hopes to accomplish under a second term, including the repeal of the Defense Of Marriage Act, which the administration has already stopped defending.

While he did not mention Republican rival Mitt Romney by name, he drew a sharp line of contrast between his own ideology and that of Republicans, promoting a theme of “togetherness.”