As interments of veterans and their dependents climb to a record level, the Department of Veterans Affairs is rushing to add burial space at the fastest rate since the Civil War.

The project is adding thousands of burial sites and vault spaces across the country. But a Nevada congresswoman is pressing the VA to add more national cemeteries, especially in Western states that now have few cemeteries but whose senior populations are growing.

"The prestige of being buried in a national cemetery is something every veteran is entitled to," said Rep. Dina Titus, a Democrat, who has been prodding the VA to open more such cemeteries in places like Nevada. It is among about a dozen U.S. states that lack a federally funded and operated national cemetery, and rely mostly on veterans' cemeteries run by states or Native American tribal governments.

Interments of veterans and their dependents have surged to nearly 125,000 in 2013 from around 37,000 in 1978, according to the VA. The increase has come as the World War II generation moved into its golden years and more categories of veterans, including some reservists, their dependents and even some of their parents, are among those authorized to be buried in VA cemeteries.

The VA maintains about 3.2 million gravesites, half a million more than in 2008, and has capacity to more than double these numbers. In 2009, the VA opened six new national cemeteries. It plans to open five more national cemeteries in coming years and is encouraging states and tribal governments to build cemeteries through grant programs.

The VA's National Cemetery Administration has requested $114 million for construction in 2014 for two new national cemeteries in Florida, and will continue planning three more in other states for the coming years.

With the expanding availability of burial sites and more veterans reaching old age, the number of projected interments of veterans is on the rise. A 2008 study by ICF International, ICFI -0.03%  a consultancy firm, had forecast that interments at national cemeteries would peak in 2010, but the VA now says it expects the peak come in 2017, with more than 135,000 interments projected for that year.

In some western states, however, it sometimes takes a long drive to reach the scattered veterans cemeteries. Janet Snyder of Las Vegas recently carpooled about an hour with a military widows group to a state-run veterans cemetery in Boulder City, Nev., where they laid wreaths at their husbands' memorial markers, an annual tradition.

Ms. Snyder, who is 73 years old and doesn't drive, said it is a "major production" to get to Boulder City to visit the memorial marker for her husband, Tom, who served in the Army for 20 years. If the cemetery were closer to Las Vegas, she said, "a lot of our members would visit the graves more often."

Steve Muro, head of the National Cemetery Administration, said the VA is providing more burial sites in the West, and that it chooses locations based on population density. The VA will add smaller burial plots where there are relatively few veterans and large cemeteries in places with greater population density, he said.

"We're trying our best to improve burial options throughout the U.S.," Mr. Muro said.

Ms. Titus said the VA should specifically add national cemeteries in states that don't currently have them. Her home state of Nevada has more than 300,000 veterans and is among the Western states that had the fastest growth of any region among people age 65 or older—which includes many veterans—according to the 2010 census, and that growth is expected to continue. For her, national cemeteries have greater cache than state cemeteries, she said.

The VA says all veteran cemeteries are maintained in the same manner and all graves are treated with the same reverence. Veterans' advocacy groups say they are more worried about expansion than whether the cemeteries are national- or state-run. But they also say the VA needs to be flexible to help underserved populations and anticipate growth patterns.

"There are times the VA should look outside its own policy to ensure geographically disadvantaged veterans have reasonable access to burial options," said Joe Davis, spokesman for the Veterans of Foreign Wars.

The VA said its system is flexible, allowing for the establishment of federally run and maintained rural burial plots when fewer than 25,000 veterans are within 75 miles of a site. Cemeteries are reserved for when 80,000 veterans or more are within the 75-mile radius. A VA official said burial plots are different from a cemetery in name only.

Eligible veterans' burial benefits include a gravesite at any of the VA's 131 national cemeteries with a headstone or marker. For service-related deaths, the VA provides as much as $2,000 toward burial expenses and some transportation costs if the person is buried in a national cemetery.

Ms. Snyder, who trekked to Boulder City on Dec. 14 to be a part of Wreaths Across America, just wishes she could be closer to her husband's memorial. On other trips there, she places a small stone at the site. "Just a sign that we were there," she says.