WASHINGTON—Outgoing Secretary of State Hillary Clinton met privately with incoming Mexican Foreign Secretary José Antonio Meade Kuribreña Tuesday to discuss the relationship between the two countries, but appeared briefly before reporters to shake hands and show the friendship they said exists between their countries.

The two countries’ transitioning administrations sought to solidify a plan of cooperation moving forward. The Senate confirmed Sen. John Kerry as Clinton’s successor Wednesday, and Kuribreña was appointed last December after the election of Enrique Peña Nieto as president of Mexico.

Mexico’s government issues a statement Wednesday saying it welcomed the discussion of U.S. comprehensive immigration reform, supporting recent policy discussion by both President Barack Obama and a bipartisan group of eight senators.

“The priority of protecting the rights of every individual, regardless of his or her immigration status, has rightly been included at the core of this debate,” the press release said.

The senators’ proposed plan includes a path to citizenship for undocumented immigrants, a condition contingent upon increased border security.

According to a Pew Research study, about 60 percent of the 11 million undocumented immigrants in the United States are from Mexico.

Immigration from Mexico has declined since 2007 because of U.S. economic instability and growing dangers with illegal border crossings, the study concluded. Border Patrol apprehensions of all unauthorized immigrations are at their lowest since 1971.