Water levels receded all along the rain-swollen Potomac and James rivers yesterday while the death toll and estimates of damage continued to rise after a week of flooding in a four-state area that authorities described as the most devastating in 13 years.

The death toll in the four states climbed to at least 43, with 21 persons known dead in Virginia, 20 in West Virginia and one each in Maryland and Pennsylvania. Forty-five persons were missing. Meanwhile, property damage estimates, still incomplete, soared above the $700 million mark in Virginia and West Virginia alone, and they were expected to go much higher.

Virginia Gov. Charles S. Robb asked President Reagan yesterday to declare sections of the Shenandoah Valley and the southwestern part of the state a "major disaster" area, qualifying residents and businesses for federal aid. He said he expected to ask such aid for two more regions of the state.

Eight counties in West Virginia have already been declared disaster areas by the president, and Gov. Arch Moore, who called the flooding the worst in his state's history, has asked for disaster declarations in 14 other counties.

In Washington, where the Potomac crested Thursday about 3.7 feet below the level reached after tropical storm Agnes in 1972, the eddying brown flood waters gouged huge chunks out of the C&O Canal towpath. All roads that had been closed by high water Thursday reopened yesterday.

Outside the city, thousands of persons remained homeless. In West Virginia alone, the floods, triggered by torrential rains Sunday and Monday, destroyed or heavily damaged an estimated 4,000 homes in the eight counties declared a federal disaster area. At least 1,800 homes were lost in three counties.

The precise number of persons displaced at least temporarily has not been calculated, but it appeared to be well up in the thousands. Earlier this week about 10,000 persons were forced from their homes in the Roanoke area. About 1,200 persons fled high water in Preston County, W.Va.

Many persons, particularly in West Virginia, remained without essential services. The flood-crippled water system in Clarksburg, W.Va., a town of 24,000, was not expected to be back in full service before tomorrow. Dead livestock and overflowing sewage contaminated other water systems in the state.

Thousands of West Virginia residents remained in enforced isolation last night as more than 100 roads remained closed by the flood waters that destroyed or damaged a number of bridges.

Red Cross workers streamed into the state from as far as Louisiana to help gather and distribute urgently needed food and clothing, but relief workers faced a "logistical nightmare" in delivering them in the flood-stricken state, one government official said.

Abandoning cars and trucks in some West Virginia locations, state officials took to helicopters to take needed provisions to beleaguered residents.

"Some of our people are talking about seeing damage like they've never seen before, and they have seen plenty of flood damage," said Bob Blair, a spokesman for the Federal Emergency Management Agency.

West Virginia property damage estimates were put at $200 million.

In Virginia, flood waters receded last night from the streets of Richmond. The I-95 bridge over the James River, a key north-south traffic artery, was reopened yesterday.

The ebbing flood waters carpeted downtown streets with silt. Here and there, rotting fruit and vegetables lay embedded in mud as the river drew back from historic Shockoe Bottom and the Farmers Market, where it had touched restaurant awnings on Thursday.

In a preliminary estimate, emergency officials said that flood damage to Richmond, where the James crested at 30.76 feet at the city locks, 22 feet above flood level, could be as much as $100 million.

Added to the $451 million estimate made for parts of Western Virginia and the Shenandoah Valley, that would bring the damage figure for Virginia alone to more than half a billion dollars.

The counties for which Robb asked the disaster designation are Alleghany, Botetourt, Franklin, Roanoke and Rockbridge. The designation also was sought for the municipalities of Buena Vista, Clifton Forge, Covington, Lexington, Roanoke and Salem.

Federal disaster assistance programs include temporary housing aid, Small Business Administration low-interest loans for individuals and businesses, food and shelter administered by the Red Cross, and help from the Internal Revenue Service and the Social Security and Veterans administrations.

Also, there is an Individual and Family Grant program for people whose needs are not met by any other agency, according to a Federal Emergency Management Agency spokeswoman.

She said there is no formal threshold for a federal disaster declaration. Rather, she said, it is based on the ability of state and local governments to cope with the damage.

In Maryland, Gov. Harry Hughes yesterday directed the state's emergency management agency to accelerate its evaluation of flood damage so he can decide whether to request federal diasaster aid.

Hughes acted in response to a letter from chief county commissioner in hard-hit Washington County, which is on the Potomac upstream from Washington.

Ronald Bowers, the county commissioners' president, said he expected that substantial damage will be found in parts of his county. One person has died in Western Maryland as a result of the flooding.

Of the jurisdictions on either the Potomac or the James, the District of Columbia appeared to be affected least. Traffic jams in and around the District were massive on Thursday, but no deaths or injuries were attributed to the flooding, and nobody was left homeless, according to Joseph Yeldell of the city's office of emergency preparedness.

Less than a million dollars in possible damage "would be very accurate," he said. City expenses would include the relatively nominal cost of sand bags and work crews, he said. On K Street NW, beneath the Whitehurst Freeway, workers were lifting sand bags from the mud-layered street yesterday and heaving them into the back of dump trucks.

Water was being pumped from the basement garage at 1000 Potomac St. NW. Building engineer Richard Pace estimated cleanup and damage costs at $20,000.

The C&O Canal was closed above Key Bridge. Officials reported washouts and other flood damage along several sections of the 184-mile route from Washington to Cumberland, Md.

Flood waters took out a 30-by-15-foot bite between Fletcher's Boathouse and Foxhall Road.

Officials of the National Park Service said the path will be closed indefinitely while damage is assessed.

Further upstream, at Harpers Ferry, W.Va., park service officials said they expected that the National Historical Park there will remain closed for several days as a result of electrical problems, possible water contamination and damage to buildings. A temporary visitors center will be opened before most of the buildings are open, a park official said.

The dollar total for flood damage in Alexandria, where the river rolled onto low-lying Old Town waterfront area streets and flooded many basements, could not be learned yesterday. Merchants along lower King Street claimed losses in stock and trade.