New Zimbabwean President Emmerson Mnangagwa greets the crowd at the National Sports Stadium during his oath-taking ceremony in Harare, Zimbabwe, on November 24, 2017.

Two U.S. senators have met with Zimbabwean President Emmerson Mnangagwa as part of an exploratory trip which could lead to the U.S. lifting sanctions on the once-pariah African state.

U.S. Senators Christopher Coons and Jeff Flake's visit to the Zimbabwean capital of Harare over the weekend was to "explore ways of strengthening the bilateral relationship," said a tweet by the U.S. embassy there. The two politicians met with the new president, as well as members of the opposition and civil society.

Coons and Flake, both on the Senate Foreign Relations Committee, are behind a proposed amendment to the U.S.' Zimbabwe Democracy and Economic Recovery Act (ZDERA). The bill details the steps which Zimbabwe must take for U.S. sanctions to be lifted, namely the holding of free and fair elections.

"The president (Mnangagwa) has made a commitment to take action, but some of the important actions required for progress towards the conditions for free and fair and credible elections have not yet happened," Coons told the media, as reported by the Zimbabwe Mail.

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Mnangagwa has said that he is committed to holding open elections in July of this year and has invited external observers to the expected event.

It is hoped that such elections could lead to the removal of U.S.-imposed sanctions on Zimbabwe, which has seen its economy crippled by decades of mismanagement under former President Robert Mugabe.

But, "Lifting U.S. sanctions is time consuming and not straightforward," Alex Vines, head of the Africa program at think tank Chatham House, told CNBC via e-mail. "The easiest way would be for the Zimbabwean government to prove that it's fulfilled the requirements of ZDERA."

Nonetheless, Coons and Flake's visit could symbolize the latest in a warming of relations between the U.S. and Zimbabwe. In March, Mnangagwa penned a column in the New York Times which highlighted Zimbabwe's newfound openness.

In February this year, U.S. chain Pizza Hut opened its first branch in Harare. The move, according to the U.S. embassy's website, "is a demonstration that American companies see attractive business prospects in Zimbabwe."