"The United States stands ready to work with Bangladesh. And we will work to enhance economic opportunities," Clinton told a joint news conference.
Clinton hailed December's election -- in which Prime Minister Sheikh Hasina won the latest rematch against arch-foe Khaleda Zia -- as "the freest and fairest in the country's history."
"Bangladeshis now have the opportunity to build on this success," Clinton said.
US President Barack Obama has made reaching out to the Islamic world a signature policy, including through a June 4 speech in Cairo. Sheikh Hasina's Awami League is strongly critical of radical Islam.
"As a country with a strong secular and democratic heritage, a record of respect for women and a Muslim-majority population, Bangladesh embodies the promise that President Obama spoke of in Cairo," Clinton said.
Moni said Bangladesh attaches "great importance to our relations with the United States."
"We consider the US as our close friend and partner," she said.
Moni said that she asked Clinton to work for duty-free and quota-free access for Bangladeshi goods to the US market.
Proposals before the US Congress would extend such trade benefits -- now enjoyed by poor African nations that meet US criteria on free elections and markets -- to less developed nations elsewhere such as Bangladesh and Cambodia.
But the measures have met resistance by some African nations, which fear they cannot compete against the Asian nations.
In a personal concern for the new government, Moni also sought Clinton's help in extraditing culprits of the 1975 assassination of Bangladeshi independence leader Sheikh Mujibur Rahman, the father of Sheikh Hasina.
Moni said some involved in the military coup may now live in the United States.
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