GUATEMALA CITY — One week after reaching a deal that would force Guatemala to absorb Central American migrants seeking asylum in the United States, the head of the Department of Homeland Security assured Guatemalan officials that the United States would invest in the country and try to sign similar agreements with at least five other nations in the region.

The contentious deal with Guatemala, known as a “safe third country agreement,” would make migrants ineligible for protection in the United States if they traveled by land through Guatemala and did not first apply for asylum there. This would deny protections to families from Honduras and El Salvador that have flocked to the United States border in record numbers this year.

Kevin McAleenan, the acting secretary of Homeland Security, told government officials and business leaders in Guatemala in a series of meetings on Wednesday and Thursday that the United States was lobbying Mexico, Honduras, El Salvador, Panama and Brazil to agree to deals similar to the one President Trump signed with the Guatemalan minister of interior last Friday.

“We do think this is a regional responsibility and a regional solution and we can’t rely on any single partner or any single initiative to address this crisis,” Mr. McAleenan said in an interview.