The letter said that after gun violence in Newtown and other places, "To refuse to take the steps we know would reduce harm is a violation of religious values so severe that we are compelled to speak out."
The NRA, which opposes the background check expansion, is encouraging its members to contact Congress, association spokesman Andrew Arulanandam said.
Leaders of the GOP-run House have said they will wait to act until the Senate passes legislation.
Democrats say background checks help keep criminals and others from getting weapons, and say keeping records of private sales is the only way to ensure that those checks are actually conducted. Currently, the government must destroy records of checks it conducts within a day, but gun dealers must maintain paper records of the transactions for 20 years.
Republicans oppose recordkeeping as a step toward a federal registry. They also argue that current laws need to be enforced better without imposing record-keeping requirements on additional gun buyers.
Since the federal background check system began in 1998, the government has received more than 118 million gun applications and turned down 2.1 million, or 1.8 percent, according to the Justice Department. The figures are through 2010.
Supporters of stronger curbs say those statistics show the large number of dangerous people denied firearms. They say extending the requirement to more sales would make it even more effective.
Opponents say broadening background checks would encourage more people to seek weapons illegally.
A 2004 survey of state prisoners involved in crimes that included guns showed that around 4 in 10 got their firearms from friends or family and nearly that many got them from unregulated street dealers. Only around 1 in 9 got them from licensed dealers.