MEXICO CITY — More than a year ago, the State Department held a meeting with bankers and Cuban officials to deliver an unusual request: please accept Cuba’s money.

The one bank that did business with Cuban diplomats in Washington, M & T Bank of Buffalo, had announced that it would no longer serve foreign missions. Cuba could hardly shop around for a replacement, not least because it is on the American government’s list of nations that support terrorism — forcing Cuban diplomats in Washington to carry out many of their transactions with bundles of cash.

Now, Cuba’s spot on the American list of states that sponsor terrorism is emerging as a major sticking point in the effort to restore diplomatic ties with the United States and reopen embassies that have been closed for nearly five decades.

On Friday, Cuban and American officials met in Washington for a second round of talks aimed at carrying out the vow of President Obama and President Raúl Castro to restore diplomatic relations. The American side reported “meaningful progress,” and more meetings were scheduled for the next few weeks on civil aviation, human trafficking, Internet connections and the delicate issue of human rights.