State officials have agreed to finance plans for upgrading Branch Avenue in Prince George's County, including the intersection at Allentown Road, the site with the highest incidence of traffic accidents in Maryland, the County Council was told yesterday.

The project, which would upgrade heavily traveled Branch Avenue in the southern part of the county, would turn the existing road into a six-lane freeway from the Capital Beltway to the Charles County line, south of where Branch Avenue (Rte. 5) joins Rte. 301.

Members of the county planning staff, quoting from a state report, advised council officials that the entire 9 1/2-mile Branch Avenue improvement will cost more than $100 million.

The planning discussed yesterday is scheduled to cost about $142,000 and is scheduled for completion in 1988, they said.

Council members Sue V. Mills and William B. Ammonett, whose districts border Branch Avenue, have complained that the state has moved too slowly in its plan to improve the road. According to state police statistics, the intersection at Allentown Road was the site of 46 accidents in 1983.

Ammonett cited as an example the speedy approval received for a project to replace the deteriorating U.S. Rte. 1 bridge over Rte. 193 near College Park. That project had not been requested by the county, but was added to the list of priority projects for 1985 through 1990 because state engineers discovered the span's weakened condition, members of the council staff said.

"We found the money for the bridge over Rte. 193 because of the safety factor," Ammonett said. "We would also like the state to find the money to do the study and accelerate construction of the intersection at Allentown Road."

Prince George's County has six of the state's 10 most dangerous roads, according to police. Montgomery County has one, Anne Arundel, two, and Baltimore County, one. County planners have said that Branch Avenue has dangerously heavy levels of traffic, especially during morning and evening rush hours.

A project to improve another dangerous Branch Avenue intersection, at Woodyard Road, already has received about $5 million in state funding for improved rights of way at that interchange. That intersection was ranked No. 8 on the state's most dangerous list.

But Mills remained skeptical yesterday about the state's plans. "I don't see this ever being improved to a six-lane highway," she said.

But Jo Ann T. Bell insisted that the council should support the state plans. "We just turned down a really good housing development Brookefield for this county because we continue to talk in circles about this road," she said.