The more important portion of this passage isn't the ocean, but is the phrase from earlier in the speech, "soffocano nel nostro mare". Literally Our Sea. This was the focus of the passage, the claim to the right or necessity to control the Mediterranean Sea. This was a link to a nationalist rhetoric which had been promoted within Italy since the late 19th century. Think of it as an Italian cultural belief akin to Manifest Destiny, but with the focus on the Mediterranean and its surrounding region.
You can find much of this detailed in the Wikipedia article on the Mare Nostrum. The section on Italian nationalist usage of the phrase has the following (emphasis mine):
In the decades following the 1861 unification of Italy, Italian
nationalists who saw Italy as the successor state to the Roman Empire
attempted to revive the term. In particular, the rise of Italian
nationalism during the "Scramble for Africa" of the 1880s led to calls
for the establishment of an Italian colonial empire, which introduced
for the first time a renewed and modern concept of Mare Nostrum:3
Even if the coast of Tripoli were a desert, even if it would not
support one peasant or one Italian business firm, we still need to
take it to avoid being suffocated in Mare Nostrum.
— Emilio Lupi
Note this was not a late (WW2 era) concept, but occurred in the late 19th century as a validation for part of the colonial efforts during the above-mentioned 'Scramble for Africa'. The quote from Lupi (from 1885), shows the primary consideration is security for the state, not trade or colonization (emphasis mine):
even if it would not support one peasant or one Italian business firm
The next section of the wiki article goes into Mussolini's repetition of the concept, over 50 years later:
The term was again taken up by Benito Mussolini for use in fascist
propaganda, in a similar manner to Adolf Hitler's Lebensraum.
Mussolini wanted to re-establish the greatness of the Roman Empire and
believed that Italy was the most powerful of the Mediterranean
countries after World War I. He declared that "the twentieth
century will be a century of Italian power" and created one of the
most powerful navies of the world in order to control the
Mediterranean Sea.
The book Italian Foreign Policy, 1870-1940, discusses the appeal of the Mare Nostrum concept, in that it reaches across political boundaries:
Of all external problems, that which found the most general consensus
was the demand for Italian security in the Mediterranean. As Zaghi
writes,
Opponents and supporters of a colonial policy were in agreement that the essential interests of Italy, her future even, lay in this sea.
Even those who would never approve an undertaking in the Red Sea...and
who affirmed a policy of conquest abroad was a contradiction of the
principles of Risorgimento, were prepared to back armed intervention
that guaranteed the vital interest of the countries in the
Mediterranean.
This attitude cut across all party divisions, from Sonnino to Branca,
'the only question that had the unconditional support of Right and
Left'
So the passage in question, and especially the use of the phrase 'soffocano nel nostro mare' is an attempt by Mussolini to appeal to an old nationalist sentiment which had historically a broad appeal across the Italian population in an attempt to unite the people behind his declaration of war on France and England, the other large navies in the Mediterranean at the time.
(Comments by @Carlos Martin point out another examination of this concept as the term spazio vitale , and its connection as mentioned above to the Nazi concept of Lebensraum)
