General Musharraf, Pakistan's president, seized power in a bloodless coup in 1999, and has reneged on a pledge to relinquish his military post by the end of 2004.
Musharraf argues that the dual roles are necessary because Pakistan needs the military's firm hand to build a democratic state and fight terrorism.
But the US-based Human Rights Watch (HRW) said a civilian government would best be able to protect human rights and allow more democracy.
George Bush, the US president, should urge Musharraf to give up his military post during his 4 March visit to Pakistan, the group said.
Brad Adams, director of the Asia division at Human Rights Watch, said in a statement on Saturday: "Turning a blind eye to Musharraf's ongoing power grab undermines the Bush administration's aim of fostering democracy in the Muslim world.
"President Bush must tell Musharraf that he can no longer count on US support to subvert the Pakistani constitution and block genuine elections."
Musharraf's term expires in 2007, and there has been much debate and speculation over whether he plans to resign from the military and seek re-election as a civilian.
This week, Bush praised Pakistan's "generally free press" and the right of Pakistanis to criticise their government. But he also said: "Pakistan still has a distance to travel on the road to democracy."
The US has been careful about criticising Pakistan because the country has become a key ally in its "war on terrorism".