The group Border Network for Human Rights said it will hold its daily morning vigils through Friday. The group wants the GOP congressman to speak with them on advancing a measure they said would help immigrants.
The move comes as immigrant advocates continue to press the congressional delegation's lone Republican to support a federal proposal that would grant immigrants in the country illegally a pathway to citizenship. Pearce has said he didn't support that measure.
Pearce, who represents a district that borders Mexico, is viewed by the GOP as a key figure in helping attract Latino voters to the Republican Party.
Eric Layer, a Pearce spokesman, said immigration reform has long been a priority for the congressman.
"Congressman Pearce has met with dozens of groups and countless individuals from throughout New Mexico and around the country regarding immigration reform, including at a wide variety of town halls, forums, and meetings throughout the month of August," Layer said. "Productive dialogue is central to Rep. Pearce's work for New Mexico, and we've always welcomed groups of all views and backgrounds to join us in sharing ideas and concerns."