Ms Metsola, 43, has a record of being anti-abortion, but has billed herself as pro-LGBT rights.
The Maltese national takes over the role from David Sassoli, 65, who died last week after a serious illness.
She is one of three women in the top EU jobs, along with the heads of the European Commission and Central Bank.
But taking questions from journalists on Tuesday, she was asked more than once about her views on women's reproductive rights.