MEXICO CITY (Reuters) - Mexico’s government on Thursday said it had deported two escaped prisoners of Yemeni origin to the United States and dismissed local media reports that the detainees were suspected militants.

The U.S. Marshals Service said in a statement the two men, identified as Kamal Qazah, 37, and Salah Mohamed, 35, were serving time in the United States for cigarette smuggling and drug dealing, respectively, and escaped from a high security federal penitentiary in Lee County, Virginia, on May 3 before coming to Mexico.

The two were detained in a hotel with a third man who said he was of Australian-Jordanian nationality and is still in Mexico while authorities check his immigration status, a Mexican government official said, speaking on condition of anonymity.

He is not wanted by the United States, the official added.

“The Yemenis were returned ... and were throughout in the hands of migration officials working with specialist groups in the federal police,” Mexico’s National Security Commission said in a statement.

Earlier, a Mexican National Security Commission official said the arrests were made in Mexico City on Tuesday at the request of U.S. Immigration and Customs Enforcement.

Officials said earlier all three men were Yemenis, and the arrests sparked Mexican media reports the men were “terrorists” - a notion which the Mexican official completely dismissed. The statement clarified that the two Yemenis were the wanted men.

Mexico has for years quietly helped the United States filter out potential Islamic militants from the tens of thousands of Central American migrants who travel through the country each year, bound for the southern U.S. border.

However, in U.S. President Donald Trump’s proposed 2018 budget, unveiled this week, the United States cuts all counter-terrorism aid for Mexico.

In the United States, some right-wing media outlets have spread the widely discredited notion that Islamic State fighters could be flooding across the southern U.S. border from Mexico.

“The Americans are not so worried by how many Central Americans get through, but rather about making sure nobody with even the slightest chance of being a terrorist does,” Humberto Roque Villanueva, Mexico’s deputy interior minister responsible for migration, told Reuters last year.