His letter was published in a state-run newspaper alongside Posner's visit to Egypt.
For years, Washington was criticized by local rights groups for turning a blind eye to police brutality and government corruption in turn for securing Mubarak as a key regional ally. Some allege President Barack Obama may be doing the same with Mubarak's successor, President Mohammed Morsi.
Posner said his visit was in fact to express to Egyptian officials Washington's view that democracy is more than just free elections.
"There is a need to build trust among Egyptians with different political views," he said, adding there are concerns "that the country is divided."
Despite calls by Posner for all parties to take part in upcoming parliamentary elections, opposition leader Mohamed Elbaradei said the coalition he leads may boycott the vote because of controversial election laws currently being debated in parliament.
The opposition alleges the laws favor the president's Muslim Brotherhood group, and says it also does not want to take part in elections during the current climate of violence.
"We will not be part of a decor in an undemocratic process," Elbaradei said in an interview on the privately-owned al-Hayat television station.
Rights activists, meanwhile, say police have used excessive force against the latest wave of protests that started on the eve of the second anniversary of the uprising that toppled longtime Mubarak.
Posner said that while Egyptian security forces are obligated to ensure public order in the face of violent protesters, they are also largely not being held accountable for torture and even deaths in their custody.
"This contributes to a climate of impunity and a lack of meaningful accountability for these actions," Posner said.
His comments came as hundreds of low-ranking policemen staged protests on Tuesday demanding they not be used as a tool for political oppression in the country's ongoing turmoil.
Dozens of policemen rallied outside local security administration headquarters in at least 10 provinces. Some of them carried signs reading: "We are innocent of the blood of the martyrs."
In the Mediterranean city of Alexandria, policemen gathered outside security headquarters shouting: "Down with the interior minister." They also chanted: "No to the Brotherhood takeover of the interior ministry," alleging that the Muslim Brotherhood is packing state institutions with its members.
Although small, the protests were a rare instance of dissent by Egypt's police force. The rallies reflect fears among many policemen of a public backlash after weeks of violent crackdowns on anti-government protests.
Associated Press writers Sarah El Deeb, Maggie Michael and Amir Makar contributed to this report.