The verse you’re looking for is Matthew 28:19,20
Therefore go and make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit, and teaching them to obey everything I have commanded you. And surely I am with you always, to the very end of the age.
That said, most Christians take great care to make a difference between evangelism and proselytising. One is supposed to be the good way to spread the gospel, and the other involves coercion, manipulation, deception, exploitation. The definition is murky enough that the Wikipedia page on evangelism fails to provide one.
But yes, it’s fairly safe to say that Jesus intended his followers to spread his words and teachings. Of all the things you could generalize Christianity as being, an evangelical faith is among the safest claims you can make.