The two held an hour-long meeting, discussing issues of mutual interest and ways to deepen relationships between the two countries, said a press release from the Chief Adviser's Press Wing.
Senator Peters and Prof Yunus discussed the reform initiatives of the current government, the reports submitted by reform commissions, and the interim government's plan to hold free and fair elections.
The government would hold elections in December if the political parties agreed to fewer reforms, said the Chief Adviser, adding that it may be postponed by a few months if political parties wanted a bigger number of reforms.
"The election will be free and fair. It will be held in a festive mood. There will be big celebrations on the election day, like the ones we have seen in the past," the Chief Adviser said to Senator Peters.Professor Yunus revealed plans for political parties to sign a July Charter once they agreed to the reforms proposed by the major commissions.
"The July Charter will set the future course of the country," he said.
Senator Peters expressed appreciation for the reform agenda of the government, saying the US was looking forward to a smooth democratic transition in Bangladesh.
He added that many Bangladeshi-origin people reside in his constituency in Michigan, including the city of Detroit. Some of them have expressed concern over the attacks on the minorities in recent months.
He also said there have been massive amounts of misinformation over the minority attacks. Some of this misinformation has permeated into the US, raising concerns among minority groups.
The Chief Adviser reaffirmed his government's commitment to upholding the human rights of every citizen of the country irrespective of their colour, creed, race, sex and gender.
He said the attacks on the minorities, notably Hindus, following the changeover in August last year were politically, not religiously, motivated, but his government has taken prompt actions against the culprits.
Professor Yunus invited the US senator to visit cities and towns across Bangladesh, extending the same courtesy to other US political leaders, journalists and activists to tour the country and know the actual information on religious harmony.
"We need your help. Please tell your friends to travel to Bangladesh. This way we can combat these misinformation campaigns," he said.
The two leaders also discussed social businesses, a world without poverty and microcredit as a tool to fight poverty both in the US and the rest of the world.