The senator flew to Cancun on Wednesday night, and was expected to fly back to Texas on Thursday following an outcry over the move. Millions of Texans remain without electricity and water after icy weather paralysed the state.
In a statement issued on Thursday, Mr Cruz confirmed that he was in Mexico, after pictures of him boarding the flight appeared on social media.
“With school cancelled for the week, our girls asked to take a trip with friends. Wanting to be a good dad, I flew down with them last night and am flying back this afternoon,” Mr Cruz said. “My staff and I are in constant communication with state and local leaders to get to the bottom of what happened in Texas.”
It is understood that Mr Cruz initially planned to return on Saturday but changed his return flight to Thursday as the outcry grew.
Texas has been hit by a power emergency since last weekend after plunging temperatures put pressure on the state’s energy grid.
The Texas Democratic Party called on Mr Cruz to resign. “Ted Cruz jetting off to Mexico while Texans remain dying in the cold isn’t surprising, but it is deeply disturbing and disappointing,” said party chairman Gilberto Hinojosa in a statement.
Mr Cruz was first elected to represent Texas in the senate in 2012. He ran for the Republican presidential nomination in the 2016 election, famously clashing with Donald Trump, who dubbed him “Lyin’ Ted”.
Yet he became one of Mr Trump’s most loyal supporters in the senate once Trump was president, echoing his claims that November’s presidential election was flawed.
There is speculation that he may run for the presidential nomination in 2024.