According to Broglio, Pope Leo XIV knew the situation of the US Church from his own experience.
"The phrase 'They don't understand us in Rome' no longer fits - because he certainly understands us," said Broglio, as reported by Vatican News on Tuesday.
With a view to social tensions in the USA, the archbishop picked up on the Pope's frequent appeals for unity.
"What unites us is the Gospel of Jesus Christ," he emphasised. Although there is great diversity within the Bishops' Conference, "when we speak to our people, we endeavour to speak with a united voice".
Like visiting a brother
The meeting between the US bishops and Leo last week was "a very pleasant one", said the archbishop. He had already got to know Pope Leo as Prefect of the Dicastery for Bishops. He now sees him as a Pope with "great experience" and "deep knowledge of the universal Church".
Broglio also reported on what it is like to meet a native American on the papal throne: "When you can speak to the Holy Father in your own mother tongue - which is also his - it creates a certain immediacy. You have the feeling of having an older brother at your side - and that is a great blessing."