Criminal and counter terrorism laws were being abused alongside restrictive media legislation and vague charges of endangering public security to limit free speech, the groups said in an open letter to the leaders.
The 15 signatories include the African offices of the International Commission of Jurists and Lawyers for Human Rights as well as women's groups and civil society organisations.
Obama, whose election in 2008 as the first black American president sparked huge expectations in Africa, has invited 50 heads of state and government for a summit which will see the greatest ever concentration of African leadership in Washington.
"Space for civil society in many countries is shrinking," the letter said.
"Many governments are using a combination of direct threats, oppressive laws and state policies to undermine the work of independent media, human rights defenders, and others seeking to peacefully express their views."
It notes that in countries such as Angola, Egypt, Ethiopia, Mozambique, Sudan, Swaziland, and Uganda "the response to peaceful demonstrations has often been excessive use of force by state security forces".
Egypt is singled out for the jailing of three Al-Jazeera journalists when they were found guilty of "reporting false news" after the ouster of president Mohamed Morsi last year.
"As part of their commitment to addressing security and development, participants at the summit must publicly condemn such actions and commit to upholding the right to freedom of expression, association and peaceful demonstration," the signatories said.
They also call on the leaders to take steps to eliminate the widespread discrimination against women in Africa which prevents their full participation in public life.
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