"Bathrooms are in this church; there are three of them, and they are free to use," he said, to some relieved nods. "And then you can see the inside of the church, too."

Tourist numbers are exploding downtown -- 11.5 million tourists visited in 2012 alone -- but public facilities have not kept pace. The memorial plaza at the trade center site, for example, has no public restrooms. So Trinity Episcopal Church, at the foot of Wall Street, and its nearby satellite chapel, St. Paul's, have found themselves de facto rest stops for many of the three million to four million guests they welcome through their doors each year.

The crush has resulted in the storied churches' most unexpected mission: its bathroom ministry. And though it means tour groups traipsing through the sanctuary to the restrooms, never-ending rolls of toilet paper and constant cleaning, it is a ministry the church says it counts as among its most important daily services to the public -- even though the church, overwhelmed, sometimes ponders if the access should be reined in.

"We believe God imbues everything, so there is a spiritual component to a building, a door, a bathroom, because of the way our bodies are constructed," said David Jette, Trinity's head verger, who coordinates worship services. "So anything we can do to assist that -- to relieve a need -- is good."

At Trinity, a graceful Gothic Revival edifice whose 25-story spire is framed by the canyons of Wall Street, visitors stream in throughout the day from the cacophony of the streets. Yet the question they ask most frequently upon entering the soaring, tranquil space is not where the body of Alexander Hamilton is buried in the churchyard, or whether the secret tunnels depicted under the church in the 2004 film "National Treasure" are real. (Alas, they are not.)

"Is there a bathroom?" is the question, and there seems to be no language barrier.

"And you always get a very positive response," Mr. Jette said, "and that look of relief!"

A daily rhythm has developed. When Trinity opens each morning at 7 a.m., many of the visitors are homeless people and others who have spent the night on the street. At 11 a.m., the tourist traffic starts to build, joined by locals attending events or visiting on their lunch hour. Not until late afternoon does the squeaking of stall doors and the whir of high-speed hand driers diminish.

It doesn't hurt that Trinity's bathrooms are nice by public-restroom standards -- cathedral ceilings, wood-framed mirrors, pedestal sinks, even stained-glass windows. The women's room has only two stalls, each with its own private sink; the men's room, roughly the same size, has stalls, urinals and a baby-changing station. At St. Paul's, several blocks north, the three unisex bathrooms are less fancy, but lines are long, because the church, which evolved into a kind of shrine to the recovery efforts after the attacks of Sept. 11, is a favorite starting and end point for tours.

Rob Cardazone, a guide with City Wonders Tours, assembled his guests this week in the sanctuary of St. Paul's before heading to the National September 11 Memorial. "I have to remind them over and over again to use these bathrooms," he said. "Otherwise you just have to tell them to hold it or they have to leave the tour."

Many tourists interviewed said they were surprised -- happily so -- to see that the restrooms were open to everyone. "We were at Starbucks, and the line was so long that we thought we would just take a chance," said Shirley Merdes, who was visiting from Denver with her grandson. "God was with us."

"I almost took a shower inside," said Andrea Guzman, 27, from Ibague, Colombia; water beaded around her neck as she headed back out to the heat.

Some statistics may help give a sense of the scale of the endeavor. At Trinity, for example, the church estimates its restrooms go through toilet paper at a rate of 6,000 feet a day and 2.2 million feet a year. Last year, about 267,000 paper towels were thrown in the trash, and 260 liters of hand soap were used. A cost estimate for maintenance -- nearly five hours of work a day -- and supplies is $92,000 a year. At St. Paul's, annual paper towel use is higher -- some 600,000 sheets -- and about a million feet of toilet paper is used. Supplies and maintenance cost about $77,000 a year.

The cost would severely tax some parishes, but not Trinity Wall Street, the Episcopal parish that includes both Trinity Church and St. Paul's. It is among the richest in Christendom, with real estate holdings estimated to be worth about $3 billion, the remaining legacy of a 215-acre land grant from Queen Anne of England in 1705. Income from those holdings and other investments was $193 million in 2013, church documents state.

Several years ago, the church's governing board, or vestry, was divided over whether Trinity was doing enough to serve the poor, given its vast resources. It had closed a homeless drop-in center, for example, replacing it with a brown-bag lunch for poor people in the Trinity churchyard twice a week.

This autumn, another direct service project, a community center called Charlotte's Place, will close, because it is within an Art Deco office complex at 68-74 Trinity Place that the church is demolishing to replace with a glassy office and condo tower more than 30 stories tall. That decision has been criticized as an example of how the church is focused too much on its own status and wealth.

Yet through the controversies, the restrooms, which the church sees as a ministry to both rich and poor, have quietly continued as a small, if vital, community service, though critics of the church say it should do more.

Given Trinity's resources, "the little blessings they are scattering are meager," said the Rev. Michael Sniffen, who is the rector of the Episcopal Church of St. Luke and St. Matthew in Brooklyn, and who was arrested in a Trinity-owned lot during the Occupy Wall Street protests.

"If they really wanted to have a bathroom ministry," he said, "they would build some sort of bathroom and shower facility for the enormous number of homeless people in New York City."

A few hours spent by the restrooms recently showed how much a part of the fabric of life they have become. A New York Police Department traffic officer rushed in to use a restroom from the chaos of Broadway, which was clogged with double-decker tour buses and road construction. An office building maintenance worker explained that each day he came to the church to light a candle, pray -- and yes, use the bathroom before heading back to work.

Robert Johnson, an impoverished older man from Sheepshead Bay, Brooklyn, comes often for the brown-bag lunch, then lingers to chat with people and wash up. "I enjoy it," he said. "It's a beautiful church."

Other famous New York churches, like Riverside Church and St. Thomas Church, also offer public restrooms. But St. Patrick's Cathedral on Fifth Avenue, which gets about five million visitors a year, made tabloid headlines this year when a visitor complained that tourists there were told to go to a building across the street.

St. Patrick's, built in the 1870s, is undergoing a $170 million renovation, but adding public restrooms is not part of the plan, said Joseph Zwilling, the spokesman for the Roman Catholic Archdiocese of New York. They would cost several million dollars to install, because upgrades to the old infrastructure would be required.

In 2012, Trinity briefly closed its restrooms because of vandalism; the church blamed an Occupy Wall Street contingent who camped outside the church for months to protest its failure to do more for them and the poor. Even now, tempers can flare when tour guides treat the church primarily as a rest stop, particularly if they try to escort large groups through the sanctuary to get to the toilets during Mass.

Every now and then, Mr. Jette said, a church leader suggests tightening access at Trinity to avoid such problems. But for now, the bathroom ministry remains part of Trinity's calling. "It's not the only thing that you would point to, but you can't ignore it," Mr. Jette said. "It's too urgent."

FOOTNOTE TO THIS STORY: Now that the Episcopal Church has established itself fully with a "bathroom ministry" we at VOL wonder if the next move is to provide a free "condom ministry" by the church.