The letters were signed by Chairman Darrell Issa, a California Republican, and Rep. Elijah E. Cummings, a Democrat from Maryland and ranking member of the committee.
Blood testing for HGH was part of the collective bargaining deal struck between the league and players this summer - but only if the union agreed to the methods.
The players' union has asked for more information about the process used by the World Anti-Doping Agency and questioned the safety and reliability of the test. The NFL would be the first major professional sports league to implement HGH testing.
"We believe the league and its players remain best positioned to implement an HGH testing regime, but concerns have been raised about the status of these efforts," Issa and Cummings said in the letters. "The purpose of this meeting is to understand the concerns of the players and the league and to strongly convey our universal interest in protecting the health of millions of younger athletes across the country."
With talks over HGH testing at a stalemate, it seemed it was only a matter of time before Congress took action. However, the invitation is voluntary and not a subpoena. No date has been set for the meeting on performance-enhancing drugs.
Goodell sent a letter to Smith before the start of the regular season reiterating the league's eagerness to begin HGH testing. At that time, the NFL also notified teams that no HGH testing will be conducted because the players' association could not agree to the terms.
The league has long disputed the union's claims that the test is not valid.
WADA handles drug testing for the Olympics and is largely accepted as the gold standard for worldwide drug testing. Smith has said he's concerned that it does not take into account the different types of bodies and conditioning routines of football players.
HGH is naturally occurring in the body. The isoform test used by WADA since 2004 - and which became more widespread in 2008 - is designed to detect synthetic HGH by measuring the ratio naturally occurring in the body against a population test. The letter also was sent to Travis T. Tygart, the CEO of the U.S. Anti-Doping Agency.
"The agreement by the NFL and its players to engage in an effort to eliminate all PEDs from the game will protect the integrity of the league as well as player health and safety," the letter says. "Most importantly, such testing sends a message to young athletes that performance-enhancing drugs of all kinds are not tolerated at the sport's highest level."