A group of prominent black conservatives is trying to help scrap a key part of the Voting Rights Act, the landmark civil rights-era legislation that enshrined the right of black Americans to have equal treatment at the ballot box.

The law was signed in 1965 by President Lyndon Johnson in the presence of civil rights leaders like Dr Martin Luther King and Rosa Parks, and it represented one of the milestone victories in ending the Jim Crow segregation of the deep south.

Now, however, a black conservative group called Project 21 has filed a legal brief before the US supreme court in support of a case aimed at overturning key provisions of the act. The bid, on which the supreme court is set to rule this summer, has been brought by the authorities in Shelby County in the southern state of Alabama.

Project 21's argument focuses on the part of the Voting Rights Act called Section 5, which holds that certain areas of the country with a history of racial discrimination when it comes to voting rights need to get federal approval before changing any of their voting procedures.

Cherylyn Harley LeBon, a former senior counsel for the US Senate judiciary committee and a co-founder of Project 21, told the Guardian that her group – which represents numerous high-profile black conservatives – supports the scrapping of Section 5 because she believes America had changed so much since the law was signed.

"Now we are in 2013, and the Voting Rights Act was something that came from a historical context. We need to update the law and this part of it is no longer needed," Harley LeBon said. She said her own father had hailed from the deep south and had left the region at times to get away from racial discrimination, but she insisted changing the act now was still the right thing to do. "Just because issues may be difficult to deal with does not mean they should not be dealt with," she said.

However, the effort to scrap part of the Voting Rights Act has met stiff opposition with many civil rights groups, especially those seeking to represent black Americans. The National Association for the Advancement of Colored People (NAACP) has come out strongly against the legal bid by Shelby County and its supporters.

Myrna Perez, a senior counsel at New York University's Brennan Center for Justice, said that changes to the law would be potentially harmful in the wake of controversial attempts at changing voting laws in many parts of the United States in recent years. "(The act) is single-handedly responsible for much of the progress this country has achieved in terms of electoral equality. Changing it would have a tremendous impact. There would be no backstop against states or localities that wanted to conduct discriminatory practises in voting," Perez said.

Last year the federal government used Section 5 to block a highly controversial redistricting plan in Texas which it had feared created extra congressional seats dominated by white voters, when in fact most of the growth of Texas' voter rolls came from minority voters, especially Hispanics.

The League of Women Voters had called the Texas redistricting scheme an "extreme example of racial gerrymandering" aimed at reducing the influence of non-white voters. The plan was blocked by a federal court in August 2012. Myrna said such events showed that the Voting Rights Act was still needed. "That happened just a few months ago last year," she said.

Harley LeBon disagreed, saying that Section 5 was an unfair intrusion by the federal government into the rights of local government to organise their own affairs and that she was happy for black conservatives at Project 21 to spark a debate on such a thorny racial issue. "This is what America is all about: having a discussion. There is a whole network of black conservatives. The Democrats do not have a lock on black support," she said.

Project 21 is sponsored by the National Center for Public Policy Research, a Washington-based foundation that says it is dedicated to finding "free market solutions" to social problems. According to its website, the NCPPP opposes environmental regulation, the influence of the United Nations and wants to drastically cut government spending.