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By Halimah Abdullah and Lauren Chadwick

In an address that offered a glimpse of the types of tensions at play as the U.S. and Cuba worked to thaw chilly relations, Secretary of State John Kerry and Cuban Foreign Minister Bruno Eduardo Rodriguez stressed Monday that reopening embassies is an important first step toward normalizing relations.

"We are determined to live as good neighbors on the basis of mutual respect, and we want all of our citizens — in the U.S. and in Cuba — to look into the future with hope," Kerry said in Spanish, which was then translated into English.

The historic shift from Cold War era relations was memorialized on Monday when Cuban officials inaugurated their embassy in Washington. Around 4 a.m. ET and with little fanfare, maintenance workers placed the Cuban flag in the lobby of the State Department alongside those of other nations with which the U.S. has diplomatic ties.

Kerry plans on visiting Cuba for the U.S. embassy opening on August 14th.

"Mr. Secretary I’ll be waiting for you," Rodriguez said during a press conference on Monday.

Related: U.S.-Cuban Diplomatic Ties Officially Restored After 5 Decades

Related: Obama on U.S. Embassy in Cuba: 'This Is What Change Looks Like'

Reopening the Cuban embassy follows President Barack Obama's call to normalize relations and economic ties between the two countries after decades of Cold War hostilities. The U.S. severed diplomatic relations with the communist island country in 1961.

The president announced in December that the U.S. was ending an "outdated approach" of isolating Cuba. In May, the U.S. dropped Cuba from its list of state sponsors of terrorism.

Deep ideological issues still remain.

Among them: thorny disputes over mutual claims for economic reparations, Havana's insistence on the end of the 53-year-old trade embargo and U.S. calls for Cuba to improve on human rights and democracy.

Rodriguez emphasized that "totally lifting of the blockade, the return of the illegally occupied territory of Guantanamo, as well as the full respect for the Cuban sovereignty and the compensation to our people for human and economic damages are crucial to be able to move towards the normalization of relations."

For his part, Kerry underscored that though progress has been made, there are still stark differences that "separate our governments".

"There are things that Cuba would like to see happen," Kerry said. "There are things the United States would like to see happen."

That much work remains to better shore up relations was evident when the two leaders spoke with reporters during a press conference on Monday afternoon.

Kerry said he certainly understood Cuba's "strong feelings" on matters on which the two nations disagree.

Rodriguez called Obama's executive actions on Cuba "limited" but "steps in the right direction."

But those steps might be met with stumbling blocks.

Some U.S. lawmakers have stridently criticized the Obama administration's efforts to repair relations with Cuba.

"While the attention may be focused today on empty ribbon-cutting ceremonies, I remain deeply concerned with ongoing human rights violations in Cuba," Sen. Bob Menendez, a New Jersey Democrat, said in a statement on Monday. "There have been over 2,800 political arrests on the island this year alone, and there is no sign the Castro regime is willing to begin respecting the Cuban people’s right to freedom of expression, independent journalism, or access to information."

Others, including several prominent Republican presidential candidates, have vowed not to repeal the embargo and pledged to roll back Obama's moves on Cuba.

Sen. Marco Rubio, R-Florida, who is Cuban American and a GOP presidential hopeful previously vowed to oppose confirmation of an ambassador to Cuba until there is a resolution on such issues as "the return of U.S. fugitives being harbored in Cuba, settling outstanding legal claims to U.S. citizens for properties confiscated by the regime, and in obtaining the unequivocal right of our diplomats to travel freely throughout Cuba and meet with any dissidents, and most importantly, securing greater political freedoms for the Cuban people."

Kerry told NBC News that congressional threats to block funding for the American embassy in Cuba and refuse to confirm an ambassador "doesn't make sense".

"I just think it's — it's cutting off your nose to spite your face," Kerry said. "And it's a shame."

You can watch more of the interview with Kerry on ‘Andrea Mitchell Reports’ at 12 p.m. ET Tuesday

Associated Press contributed.