Updated

Sen. Ted Cruz has introduced legislation that would change the name of the street where the new Cuban Embassy is housed in Washington D.C. to that of Oswaldo Paya, the Cuban dissident who died in 2012 in a mysterious car crash.

Presidential contender Cruz, a Texas Republican and son of a Cuban father, said in a press release that his measure seeks to honor Cuba’s late “leader in democratic movements” and “serves as a tribute to those who have contested the cruelty and oppression of the Castro regime.”

Cruz introduced his bill just days after the opening of the Cuban Embassy that marked a new era in U.S.-Cuba relations.

The new era began with little fanfare when an agreement between the two nations to resume normal ties on July 20 came into force just after midnight Sunday and the diplomatic missions of each country were upgraded from interests sections to embassies.

The historic shift was publicly memorialized later Monday when Cuban officials formally inaugurated their embassy in Washington and Cuba's blue, red and white-starred flag flew for the first time since the countries severed ties in 1961. In attendance were Secretary of State John Kerry and his Cuban counterpart, Bruno Rodriguez.

Oswaldo Paya, a Christian activist, died in 2012 in the eastern Cuban province of Granma in a mysterious car crash.

His daughter, Rosa María Paya, who now lives in Florida and is a prominent anti-Castro activist in her own right, contends that her father’s crash was caused by the Cuban government because, she says, his car was rammed by another and forced off the road.

On Monday she and another activist were allegedly denied entrance to a press conference featuring Kerry and his Cuban counterpart at the opening of the Cuban Embassy -- Cruz and fellow Cuban congressional members Reps. Ileana Ros-Lehtinen and Mario Diaz-Balart, both Florida Republicans, sent a letter to Kerry demanding an investigation into the allegations.

The letter, which was not signed by Sen. Bob Menendez, a New Jersey Democrat, or Sen. Marco Rubio, a Florida Republican – both of whom are also Cuban and oppose the restoration of relations – contends that a State Department official warned them not to ask questions or make comments at the press conference or they would be removed.

“How very sad it would be," the letter said, "if Ms. Payá were to find that the repressive, totalitarian tactics that have silenced so many generations of Cubans do not end at the water’s edge, but have also infiltrated our own capital.”

Over the last few months, Sen. Cruz and other members of Congress who are of Cuban descent vigorously have opposed the restoration of diplomatic relations, arguing that the government of Raul Castro continues to violate human rights and to resist all manner of democratic reforms.

They say that President Barack Obama’s decision last year to restore relations and to ease U.S.-Cuba trade and travel restrictions amounted to rewarding a dictatorship and making it stronger.

“The opening of the Cuban Embassy is yet another example of the Administration’s long, slow capitulation to oppressive dictatorships around the globe,” Cruz said in the press release. “The Castros may have come to power before the President was born, but they remain at the heart the same brutal thugs they were when they imprisoned and tortured my Tía Sonia 50 years ago.”

“There is absolutely no reason to legitimize and enrich them now,” Cruz continued, “and it is my hope that this gesture will reassure those fighting for freedom in Cuba that there are still some in the United States who stand with them.”

The Obama administration, including State Department officials, have countered that the lack of diplomatic relations between Cuba and the United States have failed to lead to democratic reforms on the island. Obama said in December that it was time to try a new approach with the Cuban government.

The Associated Press contributed to this report.

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