Morgan said federal agents arrested about 64,000 people in the southern border during the month of August.
The figures indicate a reduction since during July CBP 82,000 arrests were reported and in May a maximum of 130,000.
"The President has made it very clear that he will use all the tools available to him and this administration to address this unprecedented crisis on the southern border," said Morgan.
The CBP commissioner said the administration's policy of forcing asylum seekers to remain in Mexico for the duration of their judicial cases it has served to deter organized criminals from coordinating illegal crossings.
"They tell the cartels and this vulnerable population: the game has changed," Morgan proclaimed in the White House meeting room.
Morgan noted that the measures taken by the Mexican government work to stop the flow of migrants traveling across the country after President Donald Trump threatened to apply trade tariffs in early summer.
Morgan also said he expects the crossings to decrease further and confirmed that Washington remains "absolutely" interested in pushing for a "safe third country" agreement with Mexico.
Mexico's response came hours before Ebrard meets with Vice President Mike Pence on Tuesday with whom he will review the progress of the bilateral immigration agreement reached during the month of June.
During the last months the Mexican government has intensified the application of immigration law, ordering that about 15,000 soldiers patrol the country's northern border
The policy had previously been allowed in New Mexico and Texas, but is now suspended until a new judicial review.
This measure directly affected Central American immigrants who cross Mexican territory and, before arriving at the border, surrendered to federal immigration authorities to request government protection claiming that they are fleeing their countries for different reasons.
In photos: the overcrowding and unhealthiness suffered by undocumented immigrants at a CBP center in El Paso