The invitation was made on the first anniversary of popular pope's election, and meshes with efforts by Republicans to portray the party as more engaged on the issues of poverty and inequality that have been priorities for Pope Francis.
"Pope Francis has inspired millions of Americans with his pastoral manners and servant leadership," wrote Boehner, a Roman Catholic, in the invitation letter, noting "his tireless call for the protection of the most vulnerable among us."
Boehner noted that "these principles are among the fundamentals of the American idea. And though our nation sometimes fails to live up to these principles, at our best we give them new life as we seek the common good."
The pope has not yet accepted the invitation, but the visit would not likely be until next year. This month President Obama is traveling to Italy and will meet with the pope at the Vatican.
Congress occasionally convenes for joint meetings with the president and heads of state in the House chamber, but officials said a pope has never delivered such an address. Pope Benedict visited Washington in 2008.
Catholics remain an important voting bloc for both parties, coveted as a bellwether of the national mood.
In Congress, an estimated 160 lawmakers are Catholic, including Rep. Nancy Pelosi (D-San Francisco), the minority leader, while more than half identify with a Protestant denomination, according to the Pew Research Religion and Public Life Project.
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